The problem would be that it does not look to be cantilevered, so the deck is carrying its weight, the weight of the roof, and the possible weight of snow.
So it just kinda depends on how much weight the deck is rated for. Really most of the problem with these kinds of decks is usually moisture control.
The roof looks well engineered too. And it would also have a lighter snow load than the deck if the pitch is decent.
It is harder to shovel than the deck would have been.
The problem would be that it does not look to be cantilevered, so the deck is carrying its weight, the weight of the roof, and the possible weight of snow.
So it just kinda depends on how much weight the deck is rated for. Really most of the problem with these kinds of decks is usually moisture control.