No pros, only cons
What are the pros and cons of using grey water for flushing ?
Gray water ("galley, bath and shower water," not JUST water that's been used for dish washing or other galley use) contains soap scum, bacteria, dirt, body oils, hair, maybe food particles and cookimg debris too...NONE of which is good for a toilet pump or sanitation plumbing. No WAY should it be flushed into any Type I MSD (treatment device)--it'll damage it...and you don't want gray water in your holding tank either...'cuz gray water is MUCH harder to manage successfully (eliminate sludge, prevent odor etc) that black water (sewage).
There are other good choices: 1. a toilet designed to use onboard pressurized flush water can be safely connected to the fresh water plumibing...most are electric, but they don't consume much power and a couple of options don't cost much more than a good quality manual toilet.
2. Tee your current head intake line into your head sink drain line. This provides a safe source of clean fresh water to rinse out the whole system before the boat will sit, eliminating odor from stagnant water left to sit in the intake and pump. There's been quite a bit of discussion about this in the HeadMistress forum. 3. The least desirable choice IMO is a separate flush water tank.
As for how to deal with sea water mineral buildup in the system, that can be prevented with a weekly cupful of distilled white vinegar flushed ALL the way through the system...wait an hour, then flush a quart of clean fresh water.