It may run but the main concern after overheating is has the cylinder head warped or cracked. If it runs at least that means the piston has not welded itself to the bore. Rings may have also lost some tension and may have excessive blow-by.
I would start by checking for any signs of combustion gas getting into cooling system and any internal coolant leaks.
Vertical head will be first to overheat because it sits higher and therefore loss of some coolant will leave it partially empty.
My 916 ST4 corroded the head through the exhaust port just after the valve on the vertical head.