Chirality requires an sp3 atom with four bonds sticking out in 3D
That's a dangerous definition to use. All chirality requires is that the mirror image is not super-imposable on the original molecule. Your definition would discount e.g. axially and helically chiral molecules.
In answer to the original question, yes - if you take any carbonyl as a stand-alone (outside the larger context of the molecule) then you couldn't describe it as chiral. However, this is almost a meaningless statement - chirality is a molecular quality, not an atomic one, so you can't really talk about the chirality of a section of a molecule, only of the molecule as a whole.
Perhaps a more useful way of saying it is that the carbonyl carbon is not a stereogenic centre, since interchanging the groups attached to it doesn't lead to stereoisomers.