I say yes.
The Montevideo formula determines whether or not a country should count as a country, but it also can be applied to states. The formula consists of 4 parts.
1. Permanent population
Puerto Rico has a population of 3.194 million, which would make it more populated than 20 other states, or 40% of other states.
2. Defined territory
Puerto Rico is an island that has been inhabited by the US for over a century, and, before that, Spain. It definitely has defined land.
3. Government
Puerto Rico is controlled by the US government as a territory, however they also have local branches of power, similar to a state.
4. Relations
Puerto Rico has many friendly relations with the US.
Also, the current people of Puerto Rico don't have the same rights that many other states do, such as representatives in the Senate or electoral votes in the US elections, even though they have a large population and cultural influence on the US. Their role would be much better balanced as a US state.
I rest my case.
