Without a BB data plan you can't add any email accounts to your BB. So basically you won't get emails pushed to you. You won't have the service books to do so.
As for the web access I'm not sure if this will work or not. A while back TMO had a little loophole where you didn't need the data plan and could use Opera Mini with the correct APN and get around it. Safe to say they found out about it pretty quick and closed that loophole. And knowing AT&T which are much stricter and anal about access I doubt this is a possibility. I'm not sure since I'm on TMO so don't quote me on this.
I don't think it is worth getting a BB without getting a data plan. If you don't get a data plan with your BB it instantly cripples your BB. No Email, the main reason for a BB then you might as well get a regular phone. Web Access; you can surf the web on plenty of other phones. I mean spending 300 bucks on a phone and not use it to its full potential is just not a good idea. Hope this helps.