Yeah, though it does depend on your bank's website. I'm able to access both my bank's mobile site and its full desktop site from my Android phone, and that's on a 3.8" screen. It'd be much easier and more comfortable to access from a 7" tablet.

And if you're not happy with whatever browser is preloaded (probably the default Android browser), you can always grab an alternative browser from the preloaded GetJar Market. Opera Mobile and Dolphin Browser HD are already there, and they're both solid browsers on both phones and tablets.

Or you could find another one not in the GJ market and sideload it.