Ok, so fun fact fact. Circa 10 yrs ago I built a subwoofer wall and did exactly this.(4 18" 26. cu. ft. Ported to 35 hz via reinforced sonotube). I laid a layer of sound deadener and 2" acoustic foam tiles. Did it make a difference. Yes, but I think I built my wall like ass and it tightened everything up a bit. I'm having trouble articulating how it changed the response but I guess I could say it felt "critically damped"; whatever the hell that means.
In a larger enclosure there is going to be some cavity resonances and output at a higher frequencies. Air turbulence, material resonance, air being compressed and rarified around the baskets and motors, and port chuffing creates it. I think an interesting experiment would be to take a walled off 4th order and place tiles in the ported section. I thought of this when I was watching JerryAintloud finish the 4th in his jeep on Youtube and he said that the cabin had an "echo". I would imagine you would lose a little output but it would be interesting to hear the difference.
I'm all about that tonality life when I build a system. Anything that makes it sound better or let's me listen longer without fatigue I will go the extra mile for. The thinking is that one small change doesn't really make much of a difference but a shitload of small changes, well they change everything.