I have a base model Z with the non-Bose stereo and a friend of mine has a Bose 6 disc head unit that came out of his 350Z.. was curious if I can install this head unit in my car or not

 

IIRC... No.

BOSE uses seperate amps, etc. I'm not familiar with the stock base system.

 

nope, cant do it.... and you should be glad you dont have one from the factory.
i have a bose and it sux... bad.
it has some kind of low ohm amp and weird wiring. i wanted to add an aftermarket head unit but from what i hear its huge pain.
do a search and you'll see how unpopular the bose system is as well as the the specifics as far as the amp and wiring goes.