For audio/video APC is marketing a battery system. There is a review at EnjoyTheMusic.Com
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Yes it would and no one does.
It would require a very beefy, spendy unit to ensure that the amp had all the current it wanted when functioning normally (ie all power has to flow through the battery to provide instant cutover to back up power so effectively its a bottleneck)
APC has been making some very nice power conditioners for home theater systems the past few years, was not aware that they are now offering battery back-up as well - will have to look into it since they are the battery backup leaders.