This is a pretty nice tune and it works on it's own style.. however I wouldn't call it jazz; Jazz fusion would be a far stretch too. The tune has to have that 'swing feel'. The instruments have to be much more independent and with a more important role on the song. You can still do it from a studio with pre-recorded intstruments however I'm not very experienced with how those tools work.

http://www.youtube.com/watch?v=rsz6TE 6t7-A --- this is a nice example of how that 'swing feel' sounds like.. Just listen to some jazz and you'll get the hang of it :)