It is generally not a good idea because of potential over fill and back up. In your case it sounds like, it is not so much a question of can you as it is do you have another choice?
We easily use three times more gray water than the black water. But if you really only have room for one tank there is not much choice. How many sewer lines do you have at home?
If you have ever over filled a gray tank you discover it backs up into the lowest point. In our case it backs up into our TT's shower tub. I would not want that back up to be from the black tank.
My PUP was no black tank and gray water empties to the ground or a container.
If I installed a toilet and single tank, it would back up into the toilet before it would reach the sink height. Still not a good option.
You could opt for a cassette toilet, or a portable black tank. We bought small Coleman camp toilette for a night time pee pot in the PUP. But, more often than not we take the TT.
Good luck