Some probably do, some probably don't. We can't really say anything about that at this point.
I have a hard time imagining places like Whiskey Peak (not a Kingdom, but still) or Drum having so much of something that other places don't have that they would be politically more significant as a result. Of course, the GL's crazy climate can create conditions where some specific useful resource would come in aplenty, like a certain type of exquisite clam that could be used to make dials or a certain type of fish that is incredibly nutritious or something, but we haven't really seen anything that would point to that being the case across the board. Some particular kingdoms, though, sure. Absolutely.
The bigger problem with that line of thinking, though, I think, is the fact that the bigger a country is geographically, the more people it can usually sustain - depending obviously on the fertility of the land. And usually the more people a country has, the more likely it is to have a highly cultivated culture and an advanced level of technology, at least until the population reaches the point where the amount of people living there starts becoming a problem. Having seen countries like Goa, I think it's safe to say and assume that the bigger countries on the Blues are all just as important, if not even more important by some merit, than most of the GL kingdoms. And if that's the case, which we can only assume at this point, then crowding the Reverie with GL personalities would be a pretty serious faux pas for Oda.
Although, let's be honest here: it's probably not going to happen. Oda has been so meticulous with his world building thus far, including even people like Dragon in his story and showing how his men infiltrate other kingdoms and places we haven't even seen, that it would be strange for him to just wing it at this point.