Buick went to a firewall-mounted evaporator in 1956. By 1956, all GM was that way, except Cadillac.
1953 and 1954 Buicks had cool-air vents running through the headliner, but it was reported to be rather restrictive.
It was improved in 1955, when air came from the trunk area, through the same clear plastic tubes, and out directly to the passenger compartment. I can attest that this method is very effective to move air. I use this on my 1954 with AC.
How well did the whole system work? In my experience with a 1954 unit, because the condenser is well ahead of the radiator and built to receive air from the road and not from the radiator fan, it operates best at speed, and very poorly in slow traffic or idle. This was improved in 1955 and later.
I am not an expert at AC, but I was able to get my system to cool the car down in hot weather about 15 degrees from outside temps. So 100 degrees outside could be cooled on the highway to about 85.
What holds the system back, I suspect, is the above mentioned condenser, and the fact that these cars are not very air-tight at all. Doors and windows just don't seal like a new car does.
GM and Frigidaire were then toward the bottom of a learning curve, and there were a lot of inefficiencies to improve upon down the road...