Good question to ask. My opinion would be this: In and of itself, the noise is not the issue. The bigger thought is - if the noise is caused by a worn compressor bearing, then things will continue to deteriorate and eventually of course the air conditioning will not work at all, and the load and drag on the accessory drive could become a bigger challenge proper engine operation. Other damage could occur as a result. If internal damage occurs to the compressor, the lines could get contaminated, causing a much larger problem as well.
My suggestion would be to obtain a second opinion, asking the same questions. Use the opportunity also to determine if the noise is indeed coming from the compressor, and not just a tensioner or idler pulley.