I am reminded of when I bought my Dodge Ram 3500 in CA. Since I bought it from a dealer, it HAD to be registered in CA, titled in CA, and the CA sales tax paid, even though I was at the time a resident of Montana, with a Montana address.
The title and registration showed my name and Montana address. California was happy, they had their money.
After I had transferred the title to Montana, and gotten the Montana plates and registration, I got a nasty-gram from CA DMV stating that I had better renew the CA registration or put the truck into Non-Op status, or I would be subject to heavy fines.
I made a copy of the Montana registration, sent it to them, and never heard another word.
So, yes, the OP CAN register his RV in NM, using his ID address, if NM will allow it as CA did for me. As I previously stated, he probably should not take his RV to Idaho with the NM plates on it. If he lives close to the border, he can store it in another state no problem. Just don't allow the Idaho authorities to see it in Idaho!