I've not tested the Calendar, nor any of the corporate GMail stuff, but normal GMail push is instantaneous. Won't that be the same kind of thing?
I use Exchange for work too, but I don't have it set up on my phone. Instead, I have a rule in Outlook to forward emails to my GMail account. When an email comes in, my phone will notify me around 5 seconds before Outlook does.

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My Touch 3G - Cyanogen 2.1 Or Super E 2.1 
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