Yes, it's the browser that can be problematic. There's an old, long thread that may be worth a read: 8320 without a data plan -- What you can / can't do
My phone's browser will work over wifi without my sim card, but I already have the right service books on it since I have a data plan. You may have to do something to get the service book like call Tmobile or add a data plan for a day. Something like that.
The gmail app is very nice if it will work for your account. The only problem is it only installs over the air, so you'll have to get the BB browser to work to install it.