Simon,
By default both PHP and MySQL are setup to allow unlimited simultaneous connections, so that shouldn't be much of a problem. Besides, both are extremely fast and you're only talking about 20,000 users. Since not all those users are likely to be trying to access at exactly the same momment, the number of concurrent database accesses are probably going to be much lower than you would think.
An interesting benchmark which I read somewhere (don't ask for the link as I've since lost it๐ is that a Linux box running Apache on a PII-300 with 256 megs of ram can easily handle the combined bandwidth of 5 T1 lines. No don't take that as gospel since I can't back it up, but more than likely your existing server should do the job. That is of course one of the big advantages of using Linux, a relatively low end machine can handle large amounts of traffic and operate quite nicely as a server. Just make sure you've got lots of RAM on the box. Server's, especially database server's, love RAM๐ HTH.
geoff