replacing AC compressor

Hello,

If the A/C compressor is not seized and the pulley turns as usual, then it will not impact any other components besides having no A/C.
You do want to make sure that you are not hearing any noise from the belt and check to see that the compressor pulley (clutch) is turning as the engine is running.

Here are some helpful articles:

https://www.2carpros.com/articles/how-a-car-air-conditioner-works
https://www.2carpros.com/articles/car-air-conditioner-not-working-or-is-weak
https://www.2carpros.com/articles/replace-air-conditioner-compressor

I have attached diagrams for your reference.

Please let me know of any questions.
Thank you.