Ask your agent. Hopefully you're using your own Buyer's Agent to represent you and NOT the listing agents? When buying a short sale, I NEVER tell my buyer to submit earnest money until after we get short sale acceptance from the bank. This can be easily written into the contract. Sometimes agents just hang onto the check and hand it over to the title/escrow company at closing. Other times, they hand it to the titlecompany immediately and it gets deposited in an escrow account.
Also, in CO we have "Closing Instructions" that must be signed by both parties. This document specifies who will hold the earnest money, and who is handling closing. Do you have something like this or is it specified in the contract?