We've gone through four mods on connecting our CR110 up, just couldn't make our minds up!
The first was pseudo direct to the batteries via our CBE PC200 unit and it's fuse. Yes, you can turn it off via the thermostat and all works. Main pain was having to re-adjust each time it was switched on, and it's a bit out of sight. There were other problems but more on that later.
To save messing about on the thermostat, we put a switch in line, which was easier to use and meant the fridge control wasn't being fiddled with, does seem to flex a bit. Still have to remember to set it open when switching off for a few days/weeks, just not so easy.
The fridge has an automatic battery cut off if the voltage gets too low, doesn't flatten it, but it's low. The CBE has a cut off if the battery gets low, but it's higher than the fridge. So what can happen, and it did, was on an extended stay with poor weather and no power coming in, the fridge would switch on happily, only for the CBE unit to switch off all the other electrics. Also wasn't helped by the circuits in the CBE unit introducing an additional voltage drop which was just wasted power.
Next change was to take the CBE unit out of the equation all together, and wire the fridge up directly to the batteries via a fuse and the isolation switch. Worked a treat, fridge actually ran better and the CBE unit didn't get upset.
The final mod was to replace the switch with a relay and and put the actuating switch, with led, somewhere really easy to see and use.

Having read about lots of noise problems, first thing we did when fitting the fridge was to replace the fan with a 'QuietPC' model. Fitting the fridge with the advised ventilation works 90% of the time, but not so great once in sunnier climes when the ventilation needs to step up a cog. We have a vent in the floor below the fridge which improves things, but we're now considering an upper vent. It's really only for the sunny days in Europe but we want to enjoy cold beer and relaxation not monitoring the batteries and fretting about power. It won't be just for the fridge though, as the rest of the van gets warm, we'll improve the van ventilation first.
Running a compressor fridge, we soon realised we had built a life support system for a fridge, as it's the biggest power user we have.