What's the average number of clauses modern SAT solvers can handle?
You're asking two questions.  I'll answer your first question.

There's no simple answer.  It depends on the structure of the problem.  There are problems with millions of clauses that can be handled by a SAT solver.  There are also problems with only tens of thousands of clauses (perhaps fewer) that can't be handled by SAT solvers.

The number of clauses isn't a great predictor of whether a SAT solver will be able to solve the problem in a reasonable amount of time.

Rick Decker has answered your other question.