Nope very bad idea..
So is it possible to have a hose permanently connected to the head so that we can press a button to bring water to the head rather than extend the sink hose every time. Has anyone done this?
No toilet that's designed to use sea water should ever be connected to the fresh water system...it cannot be done without risk of e-coli contamination of the fresh water, damage to the toilet, or both..and every toilet mfr specifically warns against doing so in their installation instructions (not that anybody ever bothers to read 'em). ONLY toilets that are designed by the mfr to use pressurized flush water can safely be connected to the fresh water system.
There are safe ways to get fresh water to a raw water toilet...one is to reroute the toilet intake to tee into the head sink drain. You could keep the that seacock closed except when the sink is in use and run water down the sink to flush with fresh water all the time...but it makes more sense to rinse the sea water out of the system before the boat will sit instead.
Or, you can install a separate flush water tank...but that would require totally separate plumbing...vent and fill. The sink drain is easier.
Closing the intake thru-hull and using the shower head to add water to the bowl is NOT a good idea because running dry destroys the intake impeller in an electric toilet and damages the pump in a manual toilet because bowl contents only go through the bottom part of a manual pump, leaving the rest of the pump dry, which wears out and can even damage seals, valves and o-rings.
So the only two good solutions are the sink drain line or a new new toilet that's designed to use fresh water.