I don't think Alexander was a confederate. This
source says that he campaigned as a democrat to be a circuit judge, and was forced by the republican party to take the oath. He lost the election.
Although he was in his late twenties at the start of the war, it appears that this self-imagined military expert never bothered to serve.
According to this
source, he became an invalid in 1880 due to an "attack of paresis," which was often associated with untreated syphilis.
He is definitely a fan of McClernand, which might explain his extreme hatred of Grant.