My glass microwave plate also broke a few years ago and I never replaced it and use the microwave all the time with just a regular microwave safe plate and it's been just fine.
I also just place my coffee cup in the microwave on the metal of the microwave and it stills works fine.
So yes you can still safely use the microwave without the glass plate although some microwaves have the turntable glass plate that keeps the food moving which helps to evenly cook the food but you can always turn the food around often by hand if you want.
You can also go onto ebay and buy another either new or used glass microwave glass plate for pretty cheap but you don't have to have it in the microwave to use it.