Yes, but the human body is complicated. I would not trust a non-professional for any sort of nontrivial diagnosis. Enough people don't understand the fundamentals of medicine (look at the success of airborne and homeopathy) that crowd-sourcing is of dubious quality.

You can get second opinions, but generally it's smart to stick to doctors for them.

Of course you wouldn't follow a non-profession's diagnosis withour further support or verification. But I do think that crowd sourcing would probably be able to find and identify the correct solution faster a few experts. As long as the process allows the views of those with higher levels of knowledge to predominate then it would work. In this case I believe there would be many professionals who would devote some time to look into the matter.

Apart from you privacy the worst you are risking would be to waste some of your expert doctors time in considering some additional possibilities.