Yes, you are correct that the more districts a geography contains the more proportional the map becomes. A map of single-voter districts is theoretically the same as full PR.
More seats also mean more required minority-access and minority-opportunity districts, which is a net benefit. For example, MS gaining a 5th seat due to reallocation probably triggers a second VRA district.
Unless you literally have as many districts as voters, I think it would be more accurate to say that the more districts a state has, the more reflective they will be of the state's political geography. For example, if Wisconsin had 1,000 districts I doubt it would be possible to draw a proportional map. Whereas if Wisconsin had 2 districts, a proportional map would be inevitable.
This. Just because the limit as you approach an infinite number of districts approaches proportionality does NOT mean that more districts = more proportional.
My guess is that more seats would help Dems slightly but there’s definitely places where the opposite is true.