How many inputs does your audio interface have? If it has at least four, you can just use the tape out jacks on the 424 mkII and transfer them all at once.
Otherwise, I'm not entirely sure I understand what you're asking.
If you transfer the tracks from the 424 to the computer one at a time, you're going to have to align them in the computer and time stretch them a bit, because the 424 won't play back at exactly the same speed each time. It'll be very close, but even very close, over the course of a 3- or 4-minute song, will result in misalignment.
I'm not saying you can't do this (I've done before), but using the tape outs on the 424 mkii, if your interface has 4 inputs, is a much easier way.
But again, I'm not entirely sure I understand. What do you mean by "vs. mixing it on the tape deck, and then just mixing it down into one stereo or mono track." ? Why would you need to mix the song two times?