Its pretty much been covered by the other guys but yeah it should work. To make it easier for everyone try to record at the same bit-rate as the rest of the project.
Also, start each recording from the start of the song (even if its just recording silence until the vocals kick in) so you don't have to try and move the vocal track around to match the song later on; that way if there are any problems importing the tracks you have a quick way to match everything up.
Learned that last part the hard way when I had to 'rebuild' 6 songs in logic that were originally recorded in pro tools hd
