After thinking about this for several seconds, I would suggest that at the very most any difference at all would be very subtle. That said, how could one begin to identify such a quality?
Suppose you had an infinitely interchangeable camera system where you could change one factor at a time (like a specific lens or a specific sensor or a specific system of interior flare-reducing baffles within the camera body or even the kind of black anti-reflecting coatings within the system). Then, you had a cadre of photographers with different interests such as portrait, landscape, street, and such.
Then, you mix-and-match the work and compare a pile of un-cropped prints, say. Colour in one pile and monochrome in another to make comparison between them easier. The question at this point would be what would you be comparing?
Subject, most definitely. Definition and acutance, possibly. Focus and hyperfocal distance, yes. Style, probably depending on the photographer you might pick out similarities. We could go down the list.
In most cases I can think of, the camera format size would be the defining difference between cameras' "look" all things considered. Small formats have a look that large format cameras cannot compare or imitate with and vice-versa.
When I compare a sub-miniature shots from a Tessina or a Minox to a miniature Brownie or an instamatic to a small Nikon or a Canon to a medium Mamiya or Hasselblad to a large Zone VI or a Linhoff there is a distinct difference ("look") between each of these categories of Camera Format Size.
I'm not sure this actually answers the question posed; but, I had to give it a shot. I've identified the factor, I believe. An actual term eludes me other than the nebulous one usually used which is image "quality."