Reading the "How to Register to Vote" indicates otherwise. sosmt.gov/elections/vote/#how-to-register-to-vote

Specifically "You will need to provide a residence address or specific geographic location information from which your residence address may be determined. The residence address must be in the county in which you are registering."

This clearly allows someone without an "address" to register. In my experience identifying the Post Office on or near the tribe's land is plenty sufficient.