Hello joejoe,

It is very hard to give a definite answer to your question because a dedicated server is not the only thing that is required for a very popular site. The server settings as well as the site itself should be highly optimized to meet critical demands.

For example, 1 query to DB per request doesn't seem too much, but  providing 1000 concurrent request at any time, this results in 1000 simultaneous DB queries per each moment of time. It is a serious load even for a super duper server with 4 CPUs, Gigs of RAM and SCSI hard drives assuming that the server also has to handle web requests at the same time and maybe it requires a some type of caching of query results or script outputs.

However, an upgrade to the dedicated server would be a strong requirement for site expecting a popularity increase since it makes all server resources available for the site to use as well as gives the site owner the control under all settings of the server.

I hope this is helpful.