AC belt broke up

no just your a/c will not work and disconnect the compressor from the electrical.

The A/C will not operate, but you may also encounter an issue if you are in a cold area and need to run the defroster. Like most newer vehicles the defrost position cycles the A/C compressor to help dry the air going onto the glass. Without it you could get a fogged windshield.

I would also be concerned that if the A/C belt failed the other belt may fail as well.

I agree, if one belt has failed it is time to inspect all other belts and if in doubt replace them, the A/C belt will not stop you on the side of the road, but the alt or power steering my see you stranded. do not take the risk, replace all belts to be safe.