Connecting to multiple databases on the same host

I believe this is possible from what I’ve read online but if someone could just clarify that all i would need is to use different variables when making the connections then during the call phase assign the database name before the tables such as database1.tablename and database2.tablename name??

My real question is this however. When browsing multiple databases on the same hosting provider will it speed up the search. Essentially will I be able to search several databases at the same time.

The reason I ask this is because I am building a game and I plan on it having millions of fields and possibly hundreds if not thousands of tables, especially as it grows over time.

To speed up searching I planned on breaking everything off into their own separate database maybe a total of 100. At any given time a user will only be searching a few at a time however across the entire platform all databases will be searched continually by thousands of users. An example would be User1 will be in que for databases 1, 2, and 3 while User 2 will be in que for databases 2, 3, 4. In this scenario I would expect that User2 will instantly be able to access database 4 however will have to wait in que for User1 to finish with database 2 and 3?

Is this a wise idea? Will the databases be searched separately even though they are on the same host? Are there any more efficient ideas when working with such large database?

I plan on using PHP and actionscript to build this.