hedwards: No, they are, as Wodmarch pointed out, just a protectorarte and AFAIK there's little interest in becoming the 52nd state or even a US territory.
Avles: Puerto Rico is a US territory. And there's been significant support for statehood in PR-- 46% voted for it in the most recent referendum on the topic (in 1998).
As far as I can tell that's debatable. Puerto Rico is an unincorporated Territory of the US, which as far as I can tell is pretty much the same thing as a possession or a protectorate of the US, just like Guam, the US Virgin islands and a few others.
It surprises me a bit that Puerto Rico would be able to skip the normal step of being an incorporated Territory first, like virtually all the other states.
At present, no state has ever been an unincorporated territory and then become a full US state.
But, strictly speaking, you are correct, it is an unencorporated organized territory of the US.