Can I Keep a Listing Status as "Active" Once In Escrow?

Question: Can I keep a listing in "active" status until the buyer removes their inspection contingency? 

This would be a violation of MLS rules. The "Active Under Contract" or "Contingent" listing statuses are meant for properties that are under contract but with contingencies remaining. You can try to delay changing the status for a few days until earnest money is deposited but if you go much beyond that other agents will notice and will probably report the listing to the MLS as these things can sour the quality of MLS data.