A single cylinder engine will get hard to start. My experience has been that the engine goes inoperative before it gets to the point where damage can be done.
A multi might do that ... but if it has one weak cylinder due to a tight valve, it's quite possible that the other cylinders will drag it along once started, and there is a bigger risk of having a burnt valve.
There is no substitute for going in there, taking the valve cover off, and taking a look around.