I think you need to speak to the horses mouth and contact support for the definitive answer.
I could say yes you can or I could say no, just because it is Thursday.
So you would really need to speak to the people who can say yay or nay!
I would think that if the current domain is allowed to expire so that you effectively had no domain you would still have claim to a 'free domain' so could register another. But is your expired domain seen as the one and only free domain? I know that either way the costs would remain the same and you would not get any pecuniary advantage out of it.
So it is definitely one for a support gringo.
Opinions are my own views, not DreamHosts'.
I am NOT a DreamHost employee OK!! :@
You act on my advice at your own risk!