Hi, I happen to attend intercessory prayer group right now, I was invited once and I just stayed, and I do not have that kind of doubts you do.
I have needed prayers of others now and again, and I do again, and I know what it is like to have someone who is interceding for me with God - just like Mary did in Cana. We all need the grace of God and see - in the Lord’s prayer, Jesus taught us to pray "Thy Kingdom come, thy will be done’- this seems that these should be in the interest of God himself, yet he is asking us to pray for His Kingdom to come, as if he was relying on our prayers!
Also, nobody is saying that you cannot do the acts of mercy because you are in intercessory group, and those acts of mercy might be towards the people you meet every day and your family- it is not only clothes, food, but friendship, support, listening to and making time for others. Acts of mercy, according to st Faustina are the ones that you mentioned, but also a kind word as well as prayer.
If your reasoning was correct, do you think that God made a mistake calling so many men and women to life in convents, where they do not leave the walls of their convents, but spend the time in prayer in contemplation (well, physical work as well, but some do not go out or talk to others at all)
I suggest that you read the diary of St Faustina, one of the lessons you can learn from her is that there is nothing more pleasing to God than doing His will - if he wants you to pray for others, than do that- and since you feel drawn to that group, it might just as well be the case that God is calling you to this ministry.
And lastly, even Mother Theresa spent lots of time in prayer, she who spent so much time helping the poor and sick - because she knew that we all rely on the grace of God, and we need prayers to be able to love others.