Hi
I think it highly unlikely that your man was impressed, since this practice ended in 1814. However, it was not uncommon for men who signed on for the duration of a ships commission to jump ship (Continuous Service did not become compulsory until 1873).
Without a ships name it is almost impossible to trace your man, although if you know where and when he jumped ship you could find what ships where in the area at the time, and check their Ships Description Books to see if your man was in the crew, but this would be quite a task!!
Martin