I've seen some Blu-Ray players that can play h.264 files, which lead me to wonder: if someone was to burn a movie in the h.264 codec onto a BD-R disc, would it play in a stand-alone player?

I think you would have to look at specs on the standalone and see what formats it will play. I really dont know that much about standalones especially concerning BD discs. But google is your friend if you know what standalone you are referring too.