I use an app called NetStat (the paid version is best due to no ads, and ads = connections) which basically shows all connections your device is using, and trust me even with push off, you have loads being made all the time - this actually drains battery quite a lot since random connections eating just little bits of data randomly for no reason is unnecessary work for the phone, especially cellular data.
Also, I notice when I have these active connections my phone actually lags a little bit too...
I've developed a few tricks to make it so nothing is using data ever, and it annoys me when there is push connections on when I don't even use push, my battery lasts such a long time when my netstat list is blank
Sign out of the "Store" part in settings, being signed in (you get signed in every time you sync to iTunes) creates a push connection that keeps communicating to Apple, signing out kills this.
Turn off sending diagnostic reports to Apple
Make sure email is set to Manual in the "Advanced" part also.
Opening and closing the "Phone" app once after every reboot seems to clear a random push connection, I honestly can't explain this one.
That's about it, people also suggest adding a restriction to "Ping" but afaik this is unnecessary
I'd also like to add my phone uses 0kb data in and out over night, whereas before it would just slowly creep up, trust me 10kb-20kb or so here and there soon adds up into 1mb... which would be 1% of someone's data plan if they have 100mb total