Yes. Nevada LLCs are constitutionally permitted to do business in every state in the US. However, no matter which state a Nevada LLC does business in, its internal affairs are governed by Nevada state law. In order to do business in other states, Nevada LLCs must apply to the Secretary of State (in that state) for a Certificate of Authority, which grants permission to conduct business activity and hire employees.
Nevada LLCs may also conduct business in nearly every country. Nevada LLCs that do business in other countries should go on record with those countries through the registration process required in those countries. Frequently, the countries require document legalization or an Apostille if the country has signed the Hague Treaty. Nevada LLCs may not operate in prohibited countries listed with the U.S. Office of Foreign Asset control.