As a French native, I will have never think "je suis plein" means "I'm pregnant". And it could mean "I've eaten too much",
Maybe we can wait for other natives opinion.

http://www.cnrtl.fr/definition/plein
quote
"
♦ [Le déterminé désigne une pers. ou un groupe de pers.]
(Être) plein. (Être) rassasié. [...]
"
which mean "être plein" when the subject is someone or a group people can mean "be full" , (and the other meaning "be drunk" etc)
the "pregnant" meaning appear only in the ethymological part of the dictionnary
at the line
"7. 2e moit. xiiies. «en gestation, enceinte» (Gaufrey, 318 ds T.-L.); "
so in the 13th century.
the only time I hear it, it's when a friend of my father (a farmer) are talking about cows , cats ...

In fact as "Je suis plein" can have several, it's totaly possible, and it's part of tatoeba, to have several translation "I'm full" / "I'm drunk"

in fact this kind of "several" meaning sentences, if really the reason why we've allowed one sentence to be translated several time in the same language
I'm from France, and I would understand "Je suis plein" as I'm full, or I'm drunk, depending of the context, but It will take time to think it means "I'm pregnant",

But here as "je suis plein" in the meaning of "I'm drunk" is somewhat familiar, it's odd to use it with "no thanks" which is quite polite, so here the "no thanks" bring enough context for me to guess it's in the sense of "I'm full"

for the chinese you're right, it means "I'm full", and it has been translated by a Chinese friend of mine which live in Paris for some years now, so seems for her too it's was obvious that it means "I'm full" :)

ok so I've asked to my friends, family what they will say when they have eaten too much (the goal was to not tell them about "je suis plein" to have spontaneous answer)
they say
" J'ai le ventre plein"
"je suis repu"
"je suis rassasié"
"je suis calé"
so ok no-one said "je suis plein"
so after I've asked, if I say "Je suis plein" what you will think I'm talking about
they all answered "that you're drunk"
so even after discussing of the different meaning of "Je suis plein" they said it was a bit odd to say "je suis plein" for "I've eaten too much" (in fact i've not mentionned the english sentence) and no-one mentionned a relation with pregnant.

so my conclusion

I was a bit "polluated" by the fact I known already the "wanted" meaning, and also by the english.
"je suis plein" will mean (at least in France) => I'm drunk
no relation, in people's mind with pregnancy, it's only a really specific usage with animals for people in rural area.
So if people laughed at you it's because they will think you said "I'm drunk"

and anyway this sentence sounds odd itself because
"non merci" => polite
"I'm drunk" => familliar way to say you're drunk
(and in fact maybe you will say that about someone else "il est plein", rather than using to yourself, as it's a bit pejorative)

so I will change the sentence to
"Non merci, j'ai le ventre plein" which mean "I'm full" 100% certified by natives with blind test :p

@ck in fact it was first linked with it ^^

@sidney; in fact for the "there is no one to tell you "It kinda means that, but you might get laughed at." , it's comments goal to add these explanation :) and thanks to you people will now have a full explanation ^^.
But it's true in the future we will need to tought how to notice people that a sentence has comments/note on it to warn them "it's a translation, but you may want to read the explanation we've added"

you're welcome :)

"At its core, Tatoeba is a large database of example sentences translated into several languages. But as a whole, it is much more than that" :p