"As soon as the officer checks your ID & license (on his computer), the fact that you have a CCW is going to show up."

That's not entirely correct.

Your county sheriff's office issues your carry permit, and they are not allowed to share that information with other agencies for the purpose of a statewide database.   

You may possibly be flagged as having a carry permit if a deputy sheriff in your home county runs an ID check on you.  But information about your permit wouldn't be readily available to officers from other departments.