technically yes.
On the walkman-to-pc side, yes it can be done - I've done it lots of times since I don't have a deck. Just use stereo 1/8" to stereo 1/8" cord and you're done.
The reverse, however is problematic. For one thing, the mic is is usually mono and is meant for those small electret type mics. The preamp section on that input will overamplify the line level signal coming from the pc's line out causing nasty distortion (aside from other issues). Some walkman's have a switchable mic/line input, see if that's the case with your recorder. If not, you can always burn the recording to cd in your computer, provided you have a burner.