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)
and/or
c) It would be it's main source for creating Hypnosis.
So, that's what I think.
Hope I helped. :)
Sources: Previous answers