The answer is likely school-specific. Generally, x-ray or MRI tech courses are 2-3 year college programs that you can get into right out of high school. In these cases, a BSc in physics will not likely give you any major time advantage.
I know of some radiation therapy programs that are now incorporated into a full university degree. In these cases, a BSc in physics would definitely allow you to skip much of the required course load.
Something that I've seen in the radiation therapy career specifically (and no reason why it wouldn't also apply to x-ray/MRI tech) is that people who get in with a background in physics excel tremedously in the career. They move very quickly into leadership positions and are able to adapt to rapidly changing technologies keeping themselves very employable.