The Noam Elimelech (Parashath Balak, i believe) explains it a little differently: He says that there are those people who are not on the level to have proper intentions, proper Kavanoth, while praying. In this case their Tefillah is like a body with no soul. Similarly they perform their mitzwoth as well, without lofty intentions, and so they too are compared to a soulless body.
The Tzaddik then, through his prayer, invests the body of other people's mitzwoth with a soul -- even their tefilloth, through his deep kavanoth. In this way, the prayer of the kavanah-poor person clothes and garbs the kavanoth of the Tzaddik's prayer. This is what is meant that the poor person's prayer will wrap [the Tzaddik's prayer.]