I've been using an A500 to surf for the last 3 years (...surf the internet, not the waves... although the A500 might make a good surfboard :-D) - so yes, it is possible on an A2000.
It can be a bit slow when there are hundreds of images or tons of useless javascript. Pages with flash are a nightmare. I was shocked though that IBrowse worked perfectly with my office's Microsoft Outlook Web Access. I had expected it to fail with some stupid IE-only bs, but it worked and looked exactly the same in IBrowse on my A500 (..but 16 colour). It's amazing writing work emails from home on an A500.