Yes, I would say that you can; probably.
But this should really not be a crital point for you:
If you are paying CASH, you will be depositing the money in the Escrow Account anyway.
If you are Borrowing from a Bank and putting down a down payment, you will have to deposit that down payment anyway.
If you are going to be paying Closing Costs, you will have to deposit that money anyway.
Only if you are doing a no-down loan with no Closing costs, would you not have to deposit something.
The size of your DEPOSIT/EARNEST money determines the strength of your Offer; were you planning on backing-out of the deal in the mid-stream?