This may be a stupid question but maybe not. Maybe I am missing something. Can the Feat Battle Caster be used to allow the Bard to wear medium armor and ignore spell failure?
To be on the safe side, unless there is a printed rule somewhere that says it stacks I would opt for no it doesn't. If there is a rule, though, follow that.
I don't really think it should be a big deal, though. If you can get medium armor, you can have full plate. Just make it out of mithril. It'll cost you a bit more, but I'd rather pay the cost in mithril than burn a feat another time for most casting type characters. Besides, the mithril will make it lighter, which for most casters is an important thing with regard to encumbrance.