Yes, you still claim the total child care expense.  The FSA money that you put in the account is just not taxed.  For several years I have put the maximum in a medical FSA.  At the end of the year I still claim all medical expenses.  

Medical and child care are totally different, so I'm hesitant to apply the same rules to both.

I'm reading a lot of conflicting information online about child care credits and dependent care FSAs and if you can use both or not.