Non-electric forms of refrigeration are actually a great interest of mine, as well as refrigeration generally. I really can't say for sure if you're idea will work, but I could take a stab at it!
First thing to understand, is that an RV absorption refrigerator (Diffusion Absorption) calls for heat whenever the refrigerators thermostat calls for it. A propane flame is ignited which heats the generator (boiler) portion, and also heats the bubble pump (if it is separately plumbed). The size of the burner was specifically engineered for the refrigerator, such that the generator reaches an appropriate temperature. Not so hot or the
water in the generator will boil excessively and waste heat in the rectifier and condenser, and the bubble pump may cease to run correctly, but not so cool or flow rates internally will slow, and the bubble pump again cease due to inactivity. Getting near this temperature would make your
project more of a success. There's definitely wiggle room, so don't worry!
One way to determine this, might be to enable the electric heating element portion it probably has, in in the case of small hotel refrigerators, the only heat source it has. I would monitor both the power consumption (it will be high!), and the generator temperature. This might be best done by strategically placing thermocouples on the generator. You might have to remove the gas flame flue to do this, but make sure you reinstall for accurate readings. I'm guessing they run at somewhere between 100 to 150 Celsius. A bit of research
online will also help here.
I think temperatures like this
should be possible with an evacuated tube, especially in a parabolic trough. Something else to consider, is the need to keep these refrigerators well leveled. A slight angle can cause serious problems and early failure. You would have to find a way to circulate the heat between the heat collector and the generator. I have a suggestion.
Unless you plan on rotating the parabolic trough around the stationary evacuate tube, you can forget about adjusting for the best angle. This thing is arranged for best overall sun exposure and fixed in position. The evacuated tube is presumably angled to face south (if you're in the northern hemisphere), and the generator is elevated above, perhaps behind a wall to protect the fridge from direct sun exposure. Heat would be carried from the tube by a simple two-phase thermosiphon, probably a copper pipe with water sealed inside under a vacuum. Water carries heat extremely well, so it is probably the best refrigerant for the application. It will be in a positive pressure when heated up, but the pressure shouldn't be getting too terribly high (take precautions and understand this nonetheless). The issue now is to get the heat to the generator effectively. A simple straight pipe is not best here. I would instead, remove the flue and carefully wrap copper tubing as many times and as tightly to the generator as possible. You want good thermal contact. This will be difficult, so wrapping the coil with a thin piece of sheet metal and tightening it around the coil with tubing clamps or wire might be better. Some kind of thermal paste or putty mashed into the coils could be a plus. The top of the coil is soldered or brazed to the top end of the copper pipe in the evacuated tube, and the bottom of the coil runs to the bottom of the tube (or just enters the top of the pipe and extends to near the bottom). Wrap the whole assembly in high temp fiberglass insulation.
So when the pipe heats up the few ounces of water (you'd have to figure out an appropriate amount), it vaporizes and travels to the top of the coil where it dissipates the heat and drives the refrigerator. The vapor condenses and falls back to the bottom of the pipe to pick up more heat. I'm guessing one evacuated tube won't be nearly enough, so you could plumb several together in parallel. One of the limiting factors with this design is getting enough surface area in the generator coil (the condenser) to effectively heat it. Nonetheless, I think it could work! Maybe make an inside and outside condenser coil.
Sorry for the long post; it was fun to write though! I have many more suggestions if you want to go down this road. If this device worked, the collectors could even be placed on the roof, with lines running down to the kitchen below by using a two-phase geyser pump. The fridge will over-cool on very sunny days, so provisions would need to be made for that.
Good luck. Build it!