My S. African built boat has just that. It works, but there is also a valve on the sink drain ahead of the seacock because the suction needed for my Lavac head is too much for a sink plug. Basically, the sink is not useable without turning the valve each time. We don''t use the sink, but if we did, it would be a hassle. On the other hand, there is one less hole in the boat.
I suspect that with a large check valve on the sink, the head and sink could be used together.