I have tried this with my 4-track (a step down from yours, a Tascam 414) and yes, it works, but the sound quality isn't great. I do this mostly when I'm working on material with my partner. I use the 414 to mix his guitar, my bass, and my drum machine, run it all into the PC, and either just use that to play back or to record scratch tracks. For these purposes it's fine.
However, I also tried it for recording keeper tracks and I didn't think the results were that great. Since I have no need to record lots of tracks simultaneously (such as live drums), I just track one instrument at a time. I've gotten much better results that way.
Now, I'm not saying this 424 won't be useful. I still use my 414 on occassion, such as recording my wife's band's shows (holiday celebrations, parades, small local shows, etc.), the music at my friends wedding, any time I need something portable, etc. It was also a good platform to learn on because it covered a lot in one small unit (mixer, EQ, channels vs. tracks, sends and returns, inserts, etc.). I have no plans to get rid of mine until it dies.