Sure, people put "non-RV" appliances in trailers all the time. The biggest incentive for replacing something like an RV fridge with a small dorm-style fridge is cost. A dorm fridge will run you around $100, whereas a new RV style fridge will be $700+. So, if you are going to park your trailer in the back yard or in a trailer park, really not move it much, and always have it plugged into an AC circuit, then it is justifiable to use the cheaper appliance (ie., dorm fridge).
If you want to take your trailer on trips and maintain a cold fridge on the road, then a proper RV style fridge makes more sense. If you wanted to try and run a conventional household style fridge off of your coach batteries, you would need to beef up the system significantly (multiple batteries, solar charging system, converter, etc.) By the time you have reworked your power supplies, you could have bought a couple of new RV style fridges.
It also depends on how soon you intend to sell the trailer. Whenever I see a trailer for sale with a dorm fridge instead of a real RV fridge, the red flags immediately go up, as I conclude that this trailer has been spruced up cheaply and superficially, and the owner is trying to make some quick cash with a "flip."