Is focal length consistent between medium format camera lenses and 35mm lenses? I understand that, because of the larger image captured with MF, a 500mm lens would produce an image with the same field of view as a 35mm camera shooting with a 310mm or so lens. But if I put that 500mm MF lens on the 35mm camera, will it provide the same field of view as a 500mm native mount? I assume they'd be roughly the same, but I appreciate you entertaining what may be a stupid question.
Yup! The lens will project a larger image than your sensor (thus the wider field of view you see on a bigger thing of film/sensor), so it will magnify just like any other 500mm lens.
focal length is a physical property of the lens and does not change unless some optical unit is used to change it (Like a teleconverter or conversion lens).