More info needed.
When you say forego the inverter and batteries do you mean not have them installed or not use them for the residential refrigerator? (fyi - you want an inverter and in my opinion as many batteries as you can fit/afford)
I personally would prefer a residential refrigerator because if you get the right one (no door ice/water) they are actually VERY energy efficient. I'm not sure what coachbuilders are using today but I am personally familiar with a lot of retrofits in older class A's that use surprisingly little power. The Samsung RF 197 (or replacement) is a perfect example and is happy with modified sine wave power and is extremely efficient.
Either way, a house fridge will work fine...they hold their cool when unplugged and cool off quick when plugged back in. Going down the road you shouldn't have to turn it off (even with generator off) because the engine alternator should be able to keep up. If there is an option for a higher amp engine alternator I would get that no matter what.
1995 BlueBird BMC 37
2013 Jeep Wrangler Rubicon Unlimited
1984 BlueBird Wanderlodge FC35RB-Sold