I can't comment on the E65, but I've got an E50 in front of me. It browses the web via the provider's Internet access APN, and can send and receive email at "what appears to be" the same time.
This is somewhat at variance with what it says here:
http://www.blackberryforums.com/blac...-se-p910i.html
but I suspect the problem is me not really understanding what that thread's saying.
To use your existing Blackberry SIM card you may need to get you provider to add their Internet access APN to it (I've no idea how these things tend to be done in the US, unfortunately).