Well you need your belt for your car to run because it powers other things under the hood,
Have a friend that knows something about cars look at it, if its cracked or missing pieces on it, its a sign that it needs replacing.
Replacing it will avoid a breakdown when the belt snaps
If it snaps, you will lose power steering and steering wheel will get hard to turn and your engine might shut off, because the alternator wont be running anymore to supply power to the spark plugs and battery
So yeah, it'll run, but have a friend look at it as soon as possible
In case it snaps, use your brakes and hazard lights and pull over to the nearest shopping center or the edge of the road and call a tow truck or a friend to fix it.