Would a functional mra scan show significant cognitive impairment?

The wrong question. First, there is no such thing as functional mra. You mean functional mri. Fmri is still almost completely for research. Forget about it for now. Second, tests don't show cognitive impairment; only people do. A demented pt can have a near-normal mri, while another person can have really bad-looking brain tissue (i.e. On autopsy) and still have been sharp as a tack right up till the end.