Yes, a bad AC compressor will impact your engine. Granted, its side effects might not be immediately noticeable, but in the long run, you will begin to notice engine-related issues. This is due to the fact that the AC compressor is reliant on power from the engine to run. Should the compressor fail, it would put excess strain on the engine, thus forcing it to work harder. As such, you'll begin to notice problems like poor fuel economy. Other than that, a bad compressor might, for example, rob power from your engine, hence leaving you with poorer performance and emitting higher emissions as a result.