Probably makes sense for vascular dementia / alzheimers.
One of the 3 doctors that invented Viagra (Sildenafil) wrote a book "No More Heart Disease". The premise is that they were looking for a way to treat high blood pressure and other vascular issues, and stumbled on Viagra because of it's PDE5 inhibition properties.
My non-medical doctor understanding is:
More Nitric Oxide (NO) in the veins and arteries ---> better endothelial (inner lining of the arteries / veins) health ---> better NO response ---> less risk and chance of inflammation in the arteries (inflammation causes rupture in endothelial cells, which causes cholesterol and calcium to be sent there to plug up the damage (think of this like a scab forming to heal your hand after you get cut) --> Lower blood pressure and better vascular function.
cGMP is involved with this process, but gets destroyed by PDE5. So Viagra inhibits PDE5, helps cGMP keep active for longer, and keeps the NO and blood vessels opened up for longer. Hence... the infamous effects of Viagra
So it does seem to make sense that taking Viagra (with doctor's supervision) may help keep the blood vessels open and protect the inner linings of the arteries and keep nutrients flowing to the brain and other parts of the body. (Hence some people take semi-essential amino acids like l-arginine and l-citrulline, which are also vasodilators.)