No, Paul was writing a letter. It was written to a live person (Timothy) and to other live people who might read it. It was not written to any of the departed. Paul says "I urge, then, first of all, that requests, prayers, intercession and thanksgiving be made for everyone— for kings and all those in authority, ...". Paul is not urging the departed, he is urging live people, the audience for his letter. The assertion that this equally applies to the departed is completely fabricated by the Church. The Bible does not support it, in fact, the Bible leans against contacting the departed. Physical death is meant to be a separation. By faith, we will be reunited with our fellow Christian brothers and sisters in Christ one day. But that day isn't today. There is no logic at all to saying that since it is fine for me to ask you for prayer, it must be fine for me to pray to the departed. They are completely different things.
If the Saints are alive, as we believe they are, then they are praying for us, and this expectation is not outside of the confines of the Christian faith.
But I must agree with you, FK, that we have no biblical evidence whatsoever that saints intercede on our behalf, and specifically in resposne to our prayers.
I never pray to Theotokos or other Saints. I do thank them, whether they can hear me or not, for being the role models for us to follow and for their sacrifices.
One thing 1 Timothy 2:1-5 unequivocally proves is that the fact that Christ is the only mediator to the Father does not prohibit intercession.
As to the separation between the living and the dead, Christ erased it, at least as concerns His saints:
Every one that hath left house, or brethren, or sisters, or father, or mother, or wife, or children, or lands for my name's sake, shall receive an hundredfold, and shall possess life everlasting (Mt. 19:29)
Are we separated from the saints? If so, we would be separated from Christ also, as He is with them in the everlasting life. But no, death does not separate us from either Christ or His angels or saints:
35 Who then shall separate us from the love of Christ? Shall tribulation? or distress? or famine? or nakedness? or danger? or persecution? or the sword? 36 (As it is written: For thy sake we are put to death all the day long. We are accounted as sheep for the slaughter.) 37 But in all these things we overcome, because of him that hath loved us. 38 For I am sure that neither death, nor life, nor angels, nor principalities, nor powers, nor things present, nor things to come, nor might, 39 Nor height, nor depth, nor any other creature, shall be able to separate us from the love of God, which is in Christ Jesus our Lord. (Rom 8)God hath set forth us apostles, the last, as it were men appointed to death: we are made a spectacle to the world, and to angels, and to men. (1 Cor 4:9)