What happens in a mission if I'm missing AMORE audio files?

That depends.

If AMORE voice and radio message audio files are not found during a mission, an error message window will pop up during mission play. You can click OK to continue playing the mission. This might not be so bad if it only happens once or twice but if the mission makes heavy use of these files, you will not enjoy having the error message window constantly interrupting you.

If you're missing AMORE music track files, then nothing terrible will happen other than no music will play when it should have. OFP will not display an error message window when an AMORE music track is not found. For OFP players, this means that you're not forced to download music tracks if you don't want them. For mission makers, it means their AMORE compliant missions will play whether the player has the intended music tracks or doesn't.