For the performance the key factor is _not_ the size of the user base rather the number of "concurrent" users. Concurrent in the sense, people who did something actively within the same couple of seconds and waiting for the reaction.
Currently in the order of 50-100 concurrent users could be served by a carefully installed ordinary Intel class computer, say 3 GHz processor, 2 GB RAM, a good harddisk - given the network connectivity.
As already noted by others there are much bigger installations all over the globe. Still, if your user base of 200'000 is faily active, you too will belong to the major league of moodle installations.
There is a forum "Servers and Performance" http://moodle.org/mod/forum/view.php?f=94 dedicated to this very topic. The top thread right now is a good starting point http://moodle.org/mod/forum/discuss.php?d=54123