Not directly. However, batteries do wear out over time whether or not they're used. Also they tend to get out of condition if they're never used. So the best strategy is probably to run it off battery at least once a month or so.
2) How do people with 2 macs keep them synced other than .mac, how about itunes?
There are lots of threads about this; search. SyncTogether by MarkSpace is one option (the newest and probably most powerful one). There are many, many others.
I'm not sure how anyone can answer this if you can't be bothered to say what your usage profile is. I have an iBook and an iMac; sometimes it's really nice, but generally I probably could just get rid of both of them once I get my next notebook with a sufficiently large hard drive (the 40GB drive on my iBook is limiting).