I highly doubt a public school is going to change an offer based on a deposit.
And you likely have the merit offer already?
You can wait (if it doesn’t impact housing) if this is going to bother you but it’s likely not going to earn you a better offer.
And if you have to deposit to get in housing (as your previous note infers), then yep get it in.
There have been colleges that enhance the offers as time gets closer and there’s a thread on here I started last year - but I want to say most, if not all schools mentioned, are private.