Yes, you can track AP if you choose. You would use them just like you would on Flex so they'd need to be used in the same day.
With that said, you really don't need to use AP because if you've exercised, and you're hungrier, then you can eat more with Core. If you want to use them for non-Core items, of course that's a different story.
Sorry, Sarah...I didn't see your question until now. You can definitely earn and use AP's for non-core items. I don't think they must be used in the same day but I do think there is a recommended limit to how many one uses in a day. I'll do some research for you.