Yes. For example one of his tweets from earlier today isn't a matter of public policy, it's his opinion on the current state of affairs: https://twitter.com/realDonaldTrump/status/99928232531686604...
> It's a verified account with the description of "45th President of the United States of America".
Many people on Twitter have "Works @company" or "$TITLE as Company" on their verified accounts. That doesn't make their account the property of their employer. It's purely a declarative, factual, statement.
> When he speaks (tweets) he speaks as the POTUS. Doesn't matter if it's from the @potus account or @realdonaldtrump account.
I'm saying it does. Whether it's in a personal capacity or public capacity matters. In this case there's a clear separation too as he's got access to the @potus and he seems to use that for official business.