Interesting thought Paul. I'm sure it would make a difference. I often have the final format / composition in mind when I shoot. And, when I am using a square format it is usually a conscious decision - I don't think I've ever cropped a square image to rectangular! But if I am shooting 35mm (film or digital) or even LF, I quite often have a square format in mind. And shooting with the Leica, I often make an adjustment to the framing to either compensate for errors associated with the frame lines or because I only have one focal length with me. Another example is the Mamiya 7 which has a native 6x7 format. I never print in that aspect ratio and usually take an image intending to print square (if the re-made the Mamiya 6, I'd probably buy that!).
I think my framing style is probably most influenced by MF cameras but that depends on what I'm shooting. For candid's and grabbed images, the influence is from 35mm but for slower, contemplative shooting, it is certainly strongly influenced by 6x6.
I wonder what influences others?