Well either the zombie is trained to breathe...since breathing not only falls under autonomous body functioning...breathing like...blood pumping ...heart beating...eyes blinking is autonomous...which the zombie don't got. none. nada. nil. people got...living people...not dead ones.
Not to mention breathing presumes the need for breathe which in turn presumes life...hence ...no zombie.
Even so. a human body needs air in lungs just to barely float...and that takes effort just to maintain it in the lungs...no air in lungs ...no float...swimming helps...but air is what makes the buoyancy...so...you gotta bung 'em up...both ends.. ..or teach 'em to inhale and hold their breathe and swim...human body is not an ant body...it is not comparable in density...nor is the human body...when dead or alive.. light.. like cord wood.
https://www.youtube.com/watch?v=k2MhMsLn9B0

Now I think the distinction of "what" kind of Zombie we are talking about is really everything. Since I have only been talking about the post Romero dead zombie ...not the pre Romero live zombie..which changes everything....
What we really need here is a forensic pathologist or a Zombie expert to weigh in...
And I do not doubt that in this wide wide world someone has their doctorate in such studies...most likely in the U.S.

Gawd I love "Off Topic" forum here...where else are you gonna talk about crap A to Z ... Aardvarks to Zombies.