That is risky if you cannot grasp the thread you are left with it stuck in there.  Countersunk bolts can leave very little above deck.
If a mate has a dremel with a tiny cut off disc you can cut a slot carefully without damaging the lid if you are lucky (& then likely only cosmetically that could be fixed).
The other thing I've done is to use a small sacrificial sharp wood chisel & on an angle; dig a channel near the circumference.  Then use a sacrificial screwdriver to tap at 45 degrees in anticlockwise direction.  Has worked well a number of times.
Push when using posidrive screwdrivers.
				
			 
			
		 
			
				
			
			
				Don't you look at my accountant. 
He's the only one I've got.
			
			
		 
	
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