I don't see why you couldn't do it. Cleaning it out might be a chore to get all the scum out. At least it's not a black water tank.
I am not an expert but I don't think you can reuse that tank for anything other than cleaning the boat and maybe the head. You might be able to call an expert to sanitize the tank though, I am not sure.
You should be able to install a 12 volt pressure pump and plumb a line or 2 where you need it with pex or the marine equivalent, I think Whale is the brand. All you would need is a vent on the tank that should already be there and a filler. The filler is probably the hardest because it's gravity fed and you need to probably drill a hole on the deck somewhere for the filler inlet.
Where is the grey water tank located, and what boat model?