A late 90s monitor or newer will probably be unharmed (but also has basically zero chance of being able to accept the signal). Most will just blank the screen, or display an out of range message.
Many mid 90s monitors are dangerous to try this on, because few can display the signal, but many of them can possibly be hurt by it.
Many early 90s monitors will display the picture and very nicely, but will wrap around the left 3" to the other side of the display (showing it superimposed over the right side), and this will not adjust out, no matter how hard you try (not even if crack open the monitor and futz with it).
I have so far tested 2 early 90s 14" models with Vantage giving arcade output, and both of them did that. I went ahead and tested one of them with a Time Pilot board, and it did the same thing as it did when Vantage was set to arcade output.
Those monitors do make decent test bench monitors though, good enough to see that your boardset works, and to run through test mode on.
A scant few will display the image PERFECTLY.
The best way to test for this is to just get a comp, install Vantage, and Space Invaders and set the shortcut to run it in arcade mode (I use Vantage for this because it is small, simple to get arcade output, even on top of Windows, and is fast enough to run on anything).
Then you just hook up your "possibly arcade friendly" early 90s monitor to it, and hit your shortcut. If it doesn't come up, then hit escape really fast.