Yes, if it is fresh shot that day, I have and would. I like mine grilled. Wrap each part (four x legs + saddle) in slice of bacon. Grill five minutes, turn, grill ten minutes, turn again grill for final five minutes. Very nice. Or omit the bacon and instead smother in a whole grain mustard and bake.
Have done but not any more ...
Grey squirrels are known to carry rabies (there was a well publicised case in the US last autumn) and murine typhus, they are also known reservoir hosts for bubonic plague, all these are notifiable diseases in the UK.
Grey squirrels can also carry encephalomyocarditis, toxoplasmosis, tularemia, leptospirosis and ringworm, all of which are transmissible to humans.
They can also carry endemic relapsing fever & western encephalitis, however both these are rare in Britain and Europe.
More than enough grounds for the re-establishment of a 'national cull'.
Buggers to skin, though.