No, additional AA filtering will not harm the signal to the extent you can hear it.
For example an audio player on your computer will apply a high quality phase-preserving steep aa filtering at the nyquist frequency depending on the FILE sampling rate.
So for example you play 44.1kHz sampling rate CD audio file which the player
will apply an antialiasing filter at 20kHz, but the playback equipment might be set to 48kHz or 96kHz sampling rate,, you will hear no aliasing since the audio is properly AA filtered.
Notice that 44.1kHz /2 = 22.05kHz, that is because the steep AA filter rolls down 100db from 20kHz to 22kHz, so the audible range is not affected.
Here is a standard 44.1kHz FLAC played with AIMP player, through 96kHz audio interface:
Back to MiSTer;
If Sorgelig will be able to apply a quality AA filter to the audio data stream without taking much resources from the FPGA that would be absolutely ideal for sound.
The most common and high quality is Sinc filter with high number of taps (high order) to create a very steep roll off, but it might take a lot of resources if done in software, so a compromise is needed.
Using lower taps will bring the CPU usage down but the reflected frequencies will gradually be more audible,, so we need a good balance just enough to not hear any aliasing.