No, it doesn't. There is nothing in Luke 1:35 that even remotely hints any similarity between Mary, and the Ark. Its the reasoning of men intent on transforming the handmaid of the Lord into a divine person that imagines it so.
The Ark was so holy in fact, that if anyone where to touch it they could actually fall down and die! It was housed in the Holy of Holies, which was a perfectly clean place where the Jewish high priests could enter only once a year according to their law (See Lev. 16:2-4). So how are Mary and the Ark related? The same language that describes God's "dwelling" place for the Old Ark is used again for Mary's overshadowing by the Holy Spirit.
Are there any scriptural examples that you can give showing where someone died from touching Mary? I would love to see it, because I can't think of a single example. However, that might explain why Rome thinks Joseph never touched his wife Mary.
Are there any examples of people falling dead from touching Jesus while he was on the Earth? Quite the contrary, since power came from touching him in faith on numerous occasions. Your point has no validity.
Put another way, the Old Ark held God's Ten Commandments and could not be touched by human hands because of its holiness. Mary, the New Ark, holds the New Covenant in her womb, which is Jesus Christ. How much holier is Christ than the Ten Commandments? It only makes sense that for Mary to hold God in her womb, she too would be completely pure and without any sin.
No matter how you spin, contort, or squint your eyes, it does not square with God's Word. Mary twice acknowledged her role in the conception and birth of Jesus - a handmaid, or servant. She professed faith in God's Word spoken by Gabriel - "be it unto me according to thy Word." The Living Word (Seed) became flesh in her womb (John 1) - its no more complicated than that. There was no sexual union between Mary and God like pagan mythology. It was Mary believing and acting on God's Word. In the Kingdom of God, everything starts with the Word of God (Seed) - see Parable of the Sower, and the Parable of the Seed/Kingdom of God. (Matthew 13, Mark 4, and Luke 8)
Besides, Jesus emptied himself of his divine powers and operated as the Son of Man. Jesus - made himself of no reputation, and took upon him the form of a servant, and was made in the likeness of men. (Philippians 2:1-10, see also Hebrews 2) He operated as a man, doing no mighty works until anointed by the Holy Spirit. (Matthew 3:16, 12:17-21, Luke 4:16-21, John 1:31-33, Acts 10:38) He was made like us, so we could be made like him - born again by the incorruptible Seed, the Word of God. (1 Peter 1:13-24)
Mary herself professed faith in her Savior in Luke 1:47. Why would she need a Savior if she is sinless? The idea that she is born without sin defies scripture. If it were even possible for Mary to be without sin, why send Jesus to suffer and die? And if Mary was sinless, what about her parents, and their parents? Let the elevator go to the top.
Luke 1:47 (KJV) - 47 And my spirit hath rejoiced in God my Saviour.
The whole notion is silly. It reveals the foolishness of men who choose their own reasoning over God's Word.
Romans 3:23 (KJV) - 23 For all have sinned, and come short of the glory of God; >>> This includes Mary. All means ALL.
Genesis 8:21 (KJV) - 21 And the LORD smelled a sweet savour; and the LORD said in his heart, I will not again curse the ground any more for man's sake; for the imagination of man's heart is evil from his youth; neither will I again smite any more every thing living, as I have done. >>> All descendents of Adam are born spiritually dead.
Ecclesiastes 7:20 (KJV) - 20 For there is not a just man upon earth, that doeth good, and sinneth not.
Romans 5:12 (KJV) - Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned: >>> Read all of Romans 5, because ALL are spiritually dead.
Jesus came to destroy the works of the devil and to reconnect God to man. Adam rebelled and died spiritually, leaving all mankind spiritually dead. Their new spiritual father is satan. On this side of the cross, Believers are made alive in Christ - from spiritual death to spiritual life by faith in God's Grace. There is no other way. Only a theologian could make it confusing.
Ephesians 2:1-10 (KJV)
1 And you hath he quickened, who were dead in trespasses and sins;
2 Wherein in time past ye walked according to the course of this world, according to the prince of the power of the air, the spirit that now worketh in the children of disobedience:
3 Among whom also we all had our conversation in times past in the lusts of our flesh, fulfilling the desires of the flesh and of the mind; and were by nature the children of wrath, even as others.
4 But God, who is rich in mercy, for his great love wherewith he loved us,
5 Even when we were dead in sins, hath quickened us together with Christ, (by grace ye are saved;)
6 And hath raised us up together, and made us sit together in heavenly places in Christ Jesus:
7 That in the ages to come he might shew the exceeding riches of his grace in his kindness toward us through Christ Jesus.
8 For by grace are ye saved through faith; and that not of yourselves: it is the gift of God:
9 Not of works, lest any man should boast.
10 For we are his workmanship, created in Christ Jesus unto good works, which God hath before ordained that we should walk in them.
Hebrews 12:2 (AMP) - Looking away [from all that will distract] to Jesus, Who is the Leader and the Source of our faith [giving the first incentive for our belief] and is also its Finisher [bringing it to maturity and perfection]. He, for the joy [of obtaining the prize] that was set before Him, endured the cross, despising and ignoring the shame, and is now seated at the right hand of the throne of God.
Colossians 2:6-10 (AMP) - As you have therefore received Christ, [even] Jesus the Lord, [so] walk (regulate your lives and conduct yourselves) in union with and conformity to Him.
7 Have the roots [of your being] firmly and deeply planted [in Him, fixed and founded in Him], being continually built up in Him, becoming increasingly more confirmed and established in the faith, just as you were taught, and abounding and overflowing in it with thanksgiving.
8 See to it that no one carries you off as spoil or makes you yourselves captive by his so-called philosophy and intellectualism and vain deceit (idle fancies and plain nonsense), following human tradition (men's ideas of the material rather than the spiritual world), just crude notions following the rudimentary and elemental teachings of the universe and disregarding [the teachings of] Christ (the Messiah).
9 For in Him the whole fullness of Deity (the Godhead) continues to dwell in bodily form [giving complete expression of the divine nature].
10 And you are in Him, made full and having come to fullness of life [in Christ you too are filled with the Godhead—Father, Son and Holy Spirit—and reach full spiritual stature]. And He is the Head of all rule and authority [of every angelic principality and power].
You are complete IN CHRIST. He is the author and perfecter of your faith! You don't need the middlemen (or women) to enjoy fellowship with your Heavenly Father.
Have added you to my daily prayer list. May the Peace of our Lord be with you!