It may be more trouble than it's worth, going back and forth trying to sync up the tape machine and computer on record and playback.
How many inputs do you have on your computer?
It may be worth it for you to go for a 16 track. I have both an MSR-16 and a TSR-8, both of which use 1/2" tape, and I really can't hear any difference between the two machines as they both have DBX noise reduction. You can see a post I made on comparing these two machines here, if you're interested:
http://www.homerecording.com/bbs/showthread.php?t=170166&highlight=tsr+msr
With the 16 track, you could do all of your recording onto the tape, dump them into the computer to mix if you prefer (this would necessitate a 16 channel sound card for simplicity), and then if you still need a track or two more, you could record that within the computer.
Recording in this manner will likely give you the most consistent sound, as every track will touch tape before being recorded into the computer. The MSR-16 is an excellent recorder. I once did a three generation, internal bounce, which consisted of recording a vocal track, hitting it with effects and re-recording it onto the MSR, then taking that new track, hitting it with effects again, and re-recording it onto a new track, and there wasn't any audible signal loss or distortion.
Good luck,
-MD