A database connection begins and ends very quickly, usually in the time it takes the page to load. If your host is slow or too oversold, then database queries will take longer to execute and you will need more of them.
You should be more concerned with finding a host that limits overselling and has fast servers than with the number of database connections.
That said, 100 simultaneous connections should be fine with a good server.
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A connection to the database is made everytime a page loads. So when someone opens a thread, everything is read out of the database. WHen something is posted, its written, then re-read to view the thread. You get the point.