If the AC compresore is not fixed will it have an effect on the car long term?

I wouldn't think so. Now, if the Compressor locks up, that will cause issue. But other than that it's just acting like another pulley.

just leave it off and you will be fine if the a/c belt only runs compressor i suggest you remove it

You asked about if you didn't get it fixed , but you never stated what about the compressor is faulty. If the hub bearing is failing and it locks up or worst case snaps the nose of the compressor , you WILL lose all of your accessories could be a tad dangerous while driving. open your hood and see for yourself if there is more than one belt then reply & call me an idiot. Just in case --some manufacturers make an optional bracket with idler pulley to replace a/c compressor and keep the same OEM belt. .