Absolutely! Your LLC will be legal and valid in all 50 states. Your Montana plates will be legal and valid in all 50 states.
To our knowledge, none of our over 6,000 clients has ever been ordered by any court to pay a sales tax or a penalty on a vehicle licensed through a Montana LLC that we helped set up. While we're not attorneys and cannot offer legal advice, the key point is that it's not you that will buy the motorhome (or airplane or boat) but a Montana LLC (of which you are simply a member.)
The LLC is considered a Montana resident and, as such, resides and does business in a state with no sales tax. States with sales taxes are understandably not happy about this but that’s the way it is. Even so, It's always a good idea to research the rules and regulations in your state prior to any legal transaction.
Most states have regulations regarding the registration and use of vehicles, boats and airplanes licensed in other jurisdictions but domiciled in their state but that’s a different issue. Every state is different and we encourage you to thoroughly research your own state's policies on this matter as well. It's you that must make the decision if a Montana LLC is right for you.