Yes, warranty is transferable. If the battery has issues, Apple will replace/fix the battery/laptop.
I'll just throw in my two cents on this part of the conversation, and add, that while the original warranty may be transferable, it isn't quite so clear initially that AppleCare is transferable. One of the things that the seller has to do in order to transfer the AppleCare agreement to you is to send to Apple "proof of purchase (original sales receipt) of the AppleCare agreement." If the seller didn't buy the AppleCare agreement from an authorized seller, Apple will not honor this, regardless if there is a receipt or not. In particular, any AppleCare agreement purchased off of eBay is ineligible. Even if it was purchased from an authorized seller, they will still need to be able to produce the receipt. Consequently, they also must show proof of purchase of the MacBook as well. I have learned all of this the hard way.
Also, I think the comment above about checking the battery health is a pretty good idea as well. While the machine may have been taken care of and be in "immaculate" condition, that doesn't mean that the battery is also like new. I recommend checking the battery information under the About this Mac system report and checking the number of reported battery cycles to help gauge the condition of and life left in the battery.
Of course, none of this was in your original question. Back to what you were asking about, I would say that the $1100 is about a fair price as this is what that exact model is going for now on eBay. Of course, you could point out that he wouldn't actually get the $1100 from eBay after their ridiculous seller fees. While it is a fair price, it isn't a great price.
If it were me, I wouldn't mind spending a few hundred more and getting a new, similarly spec'ed machine that has the USB 3, upgraded processor, hd cam, new battery and a year's warranty from Apple.