Batteries are not covered by the warranty. However if a problem with the bike has caused the problem then they will change it. Don't ask how I know...
Try running the short distances without the accessories on. And get the dealer to check the electrics over. There may be an issue somewhere that you don't know about.
The alternator should be up to the job, if you look at the fuse box there's circuits for so much, if they allow for all the extras then it should be up to it.
06 America - missing, presumed in bits. With it's TBS wheel... 
09 America - It's very blue....
