My Somewhat Illogical Theory
Well, yes. The reason it's belly has a swirl on it is because of it's thin skin, and that is it's internal organs. :3
Like Lombro said, this seemed inspired by real-life frogs. However, I think the main reason it's internal organs are a big swirl is to relate to the hypnosis attack it knows.
Lombro's picture shows a frog with it's internal organs showing - and they don't look like a big swirly line. In fact, it looks more like a giant-sized atom. (xD)
I think the reason they decided to make it a swirly line was:
a) Seeing that sort of thing wouldn't appeal to children
b) It was hard to draw with the limited resources to create detailed sprites in Gen I(I)
c) It would be it's main source for creating Hypnosis.
So, that's what I think.
Hope I helped. :)
Sources: Previous answers