Okay I think I have figured out the push e-mail lag I am seeing has to do with exhibition mode. This seams to be happening over wifi and cell signal. It seams to be inconsistent as I do sometimes receive my push e-mail in exhibition mode. This is using g-mail set to as arrives.

Phone was on touchstone all night last night, exhibition set to clock mode, no e-mails when I got up this morning. Without removing from touchstone opened Dr. Podder, downloaded Adam Carolla Show got ready for work. Ready to leave for work, wake up phone still on touchstone, podcast had downloaded, no e-mail notifications. Take off touchstone, drop in pocket, phone connects to BT in car, listen to podcast on the way to work, walk into work, sit down at desk, go to plugin headphones and notice my notification light is flashing. I have 6 e-mails, going all the way back through the night.