Email and chat apps will work, but everything else will slow to a crawl at best and time out at worst.
by email you mean pop3, imap and smtp or the heavy html web client?
I doubt email would work, even with imap or pop3. I get a lot of spam per day, and imap clients typically download unread messages.
I guess you could configure it not to do that, or write your own imap client with better behavior -- on your 2G smartphone.