It doesn't sound like a good idea. I would think you would end up with a very wet greenhouse. I wanted to put a swamp cooler in my greenhouse because I have mostly orchids but I suspected the catcus wouldn't appreciate it as much. Instead, I put in misters on the orchid end that run for 2 minutes every hour.
In New Mexico, you will have to run fans and have vents or you will bake your cactus. But with a swamp cooler, you would boil your cactus. My greenhouse is small, only 23 x 6 ft. I have 6 automatic vents, run 6 or 7 small clip fans constantly AND open at least one door in summer. It still reaches 110 degrees at times. Without all the fans and open door, I suspect it could reach 130. I suspect if it were more humid along with the enclosed heat, I would have mush for cactus.