Well, I'm on all that concerned about damaging my VGA CRT monitor. I would expect they have built-in protection against that and I'm willing to take the chance.
What scares me more is when the monitor goes blank as you described, how do I know the signal I have coming out of my video card will not damage the std resolution arcade monitor. Just because it is out of range for the VGA monitor, does not guarantee it will be right for the arcade monitor.