If it's the latter, I've never tried it myself, but in theory....
If you connected your tape player into the microphone input of your soundcard, then start your recording programme (e.g. Cubase VST, SoundForge, etc.) you should be able to record the track as if you were playing directly into your PC. You'd probably experience some loss of quality, but that's ultimately down to the initial quality of the recording.
If it's the first, I really couldn't advise...I suspect that as it's in "record mode", you might be by-passing the output channel and therefore you might not be able send the signal to your PC. As I say though, I'm no expert, so hopefully someone else could clarify that. (I'd be interested to know if it's possible myself actually as it's an interesting idea!)
Anyone care to shed some light?
Don't worry too much about me, ignore me long enough and I'll go away.