This article will be very brief because I just want to note down some thoughts first.

I think that the Blood Elves never would have joined the Horde. There are a few reasons for this. The first major one is that the Horde was a former enemy, while the The Alliance was a former ally. The second major one is that the Horde already housed the Forsaken by the time they joined.
The Forsaken are the remnants of the Scourge, which destroyed Lordaeron and Quel'thalas. There is no way that the Blood Elves would emotionally want to associate with a faction that took in the people responsible for their suffering.

As such, I think it would actually be most reasonable for the Blood Elves (and the High Elves honestly) to have joined the…Scarlet Crusade.