I wear progressives. I have no doubt that it has an effect on the view, but the image processing of our brain does a pretty good job of masking visual discontinuities. If one wears glasses, let alone progressives, the peripheral view is interrupted by the edge of the lens and the frame. Somehow we get over that pretty quickly. If one changes prescriptions or frames, it might take a day to adjust to a slightly different 'distortion' of the field, and then it becomes the new normal.
Fortunately, with binoculars, the field of view is severely limited, and the apparent field is also constrained, so the useful, coherent image is confined to whats visible within the field stop, in which case the 'distortions' added to one's default image appear to be solely the properties of the binocular itself.
I'm sure there are cases where either prescription, lens size, and/or eyepiece diameter, or possibly a huge AFOV, could impact the image through progressives in a more distracting fashion than what I've encountered so far.
Bill
(who is thankful there are binoculars that work for eyeglass wearers)