Running VoxAtc and st. fs sounds on two different soundcards, so that I can get ATC on my headset, but was wondering if there exists any software that can run the TTS voices through a filter to add background noice to replicate the poor sound quality in real life?

If you are running VoxATC X in FSX you can select four voicesets. Get the 8Khz Cepstral voices and set for the aircraft voices, use the 16Khz for the controllers.