I you're on an iPhone there's already a couple of other push connections that keep active too. Apples push notification service is just long-polling HTTP for example, I don't think it shares the same connection with iMessage either.
I can't pretend to know anything about IMAP or Exchange, but one would assume that push uses less than polling the email server every 5-15 minutes.
Interesting. I wasn't sure if Apple multiplexed their persistent sockets or not. I wonder how the baseband optimizes persistent connections. I suppose it doesn't have to do much of anything since the sockets aren't actively sending data.
I don't know really, I just remember seeing a bunch of long polling connections when I was using an interception proxy last. Some to Google, and some to Apple. I can't imagine the carriers particularly enjoy it, I imagine the connection drops and is re-established on quite a regular basis, it must put load on their towers.
I can't pretend to know anything about IMAP or Exchange, but one would assume that push uses less than polling the email server every 5-15 minutes.