You should be able to transfer and line the tracks up in your DAW after the fact.
The 4trk playback will probably have issues with playing back at a consistent speed and there will however be drift. If your buddies can do their overdubs in sections (like verse, chorus, intro, etc), you can edit and nudge each section easier. Editing or assembling the different takes into time probably wouldn't be too hard but it will most likely be more involved than transferring and lining up the beginning.
The different machines shouldn't be an issue (other than them being different machines with varying sonic characteristics). It sounds like that would be desirable in your situation.
Best,
jonathan