Can I have a glass bed with only the center heated?
If you're using borosilicate glass (aka pyrex) then it won't crack. You can get squares of ~20x20 cheaply off aliexpress.

If you're using window glass, picture frame class etc then you might have issues with cracking, it will depend on lots of factors like the wattage of your heater and the temperature of the room.

Your biggest problem will be that the bed heats very non-uniformly, which is unlike to give good print adhesion. I'd suggest a sheet of aluminium underneath the glass if possible, it will allow much more even heating.