Absolutely, I believe others recognize our faith by our deeds and James 2 makes that point very clear:
14 What good is it, my brothers and sisters, if someone claims to have faith but has no deeds? Can such faith save them? 15 Suppose a brother or a sister is without clothes and daily food. 16 If one of you says to them, “Go in peace; keep warm and well fed,” but does nothing about their physical needs, what good is it? 17 In the same way, faith by itself, if it is not accompanied by action, is dead.
A dead faith is a faith that is unproductive, it is unobservable by others. The example he uses is in finding a brother cold and hungry and telling him, "Go in peace be warmed and filled.", I'll pray for you, in other words. Does that do him any good? Or is it better to take him in and give him clothes and feed him a warm meal? That is faith in action. It is made manifest by the deeds we do for others. The further example of Abraham being made righteous. We know from Scripture that Abraham believed God and it was counted to him as righteousness. He was justified by his faith before God and his actions proved that his faith was genuine. It has always been that way with God. That is why without faith it is impossible to please him.
But did God need to see Abraham's actions in order to know he has faith? No. God sees the heart of man, he alone knows if faith is real. We can only see the outside and we can only observe a person's actions. We SHOULD be able to know them by their fruits, Jesus said, but I think we can agree that outward manifestations of goodness do not necessarily mean the heart is really changed. God desires we follow him in living a holy life set apart from the world, but only he knows our true motivations.
Can such faith save them?
And, why do we need others to see our faith? Can others save us?
Matthew 6:1-4 (But) take care not to perform righteous deeds in order that people may see them; otherwise, you will have no recompense from your heavenly Father. When you give alms, do not blow a trumpet before you, as the hypocrites do in the synagogues and in the streets to win the praise of others. Amen, I say to you, they have received their reward. But when you give alms, do not let your left hand know what your right is doing, so that your almsgiving may be secret. And your Father who sees in secret will repay you.
Faith compels works. If one has faith, one has works and one does these things to glorify God and not himself and not as proof of faith to others.
Works are born from love of God and love of neighbor.
The two commandments Jesus cites as the greatest.
It is not that by my works I will be saved, for I am saved only because Jesus died for my sins. But, if I believe, then works are a part of that belief, that faith. One is not true without the other.
If you are doing works so that others may see your faith, you are doing them for the wrong reason.