Set List Maker can receive MIDI in the background, but only as long as it is still running in the background. Currently it will keep running indefinitely if it is playing audio, but only for 5-10 seconds otherwise. So if you are playing audio, it should work fine. If you are not playing audio, you should be able to make a very quick switch to another app to do something and then switch back again. But if you need to keep running in the background indefinitely with no audio playing, that doesn't work.
This should be possible because other MIDI apps do it, but I haven't figured out how. I can look further into it if you have a need for that.