Put battery on "storage" while priming fridge?

I use a BatteryMINDer INTELLIGENT battery maintainer to keep the engine batteries charged.

Engine (chassis) batteries are ISOLATED from each other.

I turn my house batteries off - when in storage.

In storage I am connected to shore power - so even with the house batteries turned off - the charger/converter supplies 12vdc to the "house" (and the fridge runs fine, as long as there is shore power).

12V DC voltage needed to operate fridge on 120V AC electric element or Propane.
The DC is used as control circuit

AS for priming the fridge.......not sure what you mean by that.
IF you are referring to getting propane to flow------turn on/light off stove top burners on high to get propane flow established and place a demand on LP regulator. Then turn fridge ON---helps when propane has been valved out for any period of time. Fridge uses very little propane so it can take several attempts when you haven't established flow.

If by priming........you mean get fridge to operate.
That is a process of using heat source to vaporize ammonia which is then condensed into a very cold liquid which then sucks up (absorbs) heat from the freezer and food section compartments. This takes time initially to have a cooling effect

SO
Good 12V DC voltage
Propane flow
Time (8-12 hrs)

AND only operate fridge when it is LEVEL. Otherwise DAMAGE/PERMANENT

We usually run a cord from a 15amp outlet using an adapter it provides enough power to cool the refrigerator. The power incoming on my rehall goes to converter suppling 12v control power and 110v to refrigerator I would not run an a/c or microwave in this configureation but this is how we cool our refrigerator before use. It save a little propane too.

The fridge should be connected to the RV house batteries
not the engine battery
Be sure you have the fridge set to gas aka l.p. not automatic
Most fridge's now are only two way, but a few three way using dc power do exist, and that mode really sucks power
Fridge should need very little power just for control board and gas valve, any battery that can't last days in that mode is bad
What is your RV and what is the make and model of the fridge

PS: we always called it Pre-cooling the fridge
never heard it called priming, it does take time for an absorption fridge to cool, as much as 24 hrs, although 12 will usually be enough

The fridge is powered by the house battery. The engine is started from the chassis battery. The fridge should not be causing the chassis battery to run down.

If the motorhome had not been run for awhile last time, the chassis battery probably was weak just from sitting and from the usual slight constant loads on it. Typically the chassis battery is not charged by the converter or anything else when plugged into shore power. For long-term storage, it's best to disconnect the chassis battery or provide some means of keeping it charged (a small solar charger, a float/maintenance charger, or a gizmo such as the Trik-L-Start that steals a power from whatever is keeping the house battery charged to keep the chassis battery up).

the fridge needs 12 volts to run. If the fridge made the battery run down in one night something is wrong with your battery or other more things were on then just the fridge.