Kermit is a born leader, but a reluctant one. Looking at Kermit's long history in entertainment, I think you could conclude that Kermit's dream was simply to entertain people and make them happy by being the cause of laughter and pleasure. There are many creative types like that, who want so sing, act, write, draw, sculpt, etc. Unfortunately for Kermit, he sort of became the de facto leader of a group who also had dreams of entertaining. Anyone who has worked in the arts will tell that that--after a few years--their new, REVISED dream is to simply get to do the art they want to pursue and let SOMEONE ELSE handle all the messy business parts. That's why most actors and writers have AGENTS, and publicists, and accountants, etc. But Kermit is really the only one who can really see the potential in the entertainers that he works with, and there's never any money to hire anything done, so...he does it himself, using the people and abilities at hand. Scooter--the annoying teen-aged gofer who was foisted onto him by the theater owner, J. P. Grosse, becomes Kermit's right-hand man (or left-hand man, if you prefer). Fozzie, who was Kermit's best friend, becomes the encourager of the group. Piggy, the object of his desire and romantic intentions, becomes the break-out star. Rowlf becomes the music manager--of sorts. It's not perfect, but it works, and it takes a lot of effort to keep that "flying umbrella" aloft.
It also takes a lot of time, so Kermit is not likely to just drop everything and jaunt off to the Caribbean (unless, of course, there's a film to be shot there). Instead, he's back at the theater fixing the hole in the wall from Gonzo's cannon, or making sure that Honeydew's latest invention isn't running amok.
So...is Kermit adventurous? Does he go looking for adventure?
My NON-answer would be--he doesn't exactly have to, does he? Like water, adventure seeks its own level, and Kermit's usually knee-deep all the time. (Knee-deep, knee-deep. Um, it's a frog joke.) So while Kermit doesn't usually go seeking adventure, he sure knows how to deal with it when it shows up.
Pepe: So, does this mean, like, jes? The frog is adventurous?
Ru: Well...he's romantically involved with Miss Piggy....
Pepe: ¡Ay, caramba! That's means jes.
Ru: There.