It would work, but only if the A320 liveries is set to be usable for Air Traffic. Most livery creators don’t bother with making them work for AI. But some do. What I usually do is actually standardise all my liveries to always have AI model assign to them, so all liveries that I downloaded works for both A320 and A32NX flyable, and also A320 AI traffic.
But at the same time you need to download and install the Generic A320 Traffic mod that I linked above so that the old generic models gets disabled, and the sim uses the A320 as the only generic aircraft, and with all your A320 liveries that’s set to work with AI Traffic, the sim will use it.