I'm not 100% familiar, just stating what I have/use. My iPhone does use IMAP with push, and guess what? It uses _a lot_ of battery. Apple is very good at giving you updates that make it worse even.

I believe iOS 5 made the push function way worse than it was in iOS 4, at least in my experience. iOS 6 even worse than 5, and I haven't upgraded to 7 because I need to read yet again the T&C's and I can't be asked.

My N9 (that's my personal phone), however, uses a schedule, but not for technical reasons, I just don't want ot be bothered every-single-time I get an email :-)