Very little. The only way the db would be accessible would be from either of the systems. So one would either have to hack into one of the systems, or they would have to successfully spoof the remote system and also know the username and password to use for phpbb. I would say there's a much greater likelyhood of there being a security hole in phpbb.
Something to note is that this traffic will open. That is someone could intercept it and trick your remote instance into getting the wrong data. If you're really paranoid an alternate setup would be:
1. Limit access to phpbb's db to localhost
2. Tunnel using ssh from remote host to db host (forward port x to 3306) (of course you'll be using your 16mb DSA for this... so login may take a couple of millenia (jk) )
3. set first phpbb to access db from localhost:3306
4. set second phpbb to access db from localhost:x (where x is the port used earlier)
Presto! Military grade encryption. Now there's no possibility of spoofing or interception of data. Of course, if you're not doing phpbb over https this is all rather useless.