IsDatabaseUp returns true or throws exception
The naming convention Is… implies that the function is a predicate, returning either true or false.

If you wanted to throw an exception when the database is down, then you might name the function RequireDatabaseUp(), returning void, instead.  But that seems silly: why not just try performing a real SQL operation instead?

In summary, if you want to provide a function whose sole purpose is to determine whether the database is available, make it return true or false.  If you prefer to have an exception thrown on failure, don't bother providing such a function at all.