indeed, you don't become a general without having some kind of political instincts. Lee, for whatever his personal dislike of politicians, had political instincts, indeed, he might have even entered post-bellum confederate politics as the only alternative to a true politician like Breckinridge.
Even Washington played politics. Hell, he had to, hell he was playing politics in 1754 just to get a damn red coat commission. and although Lee revered Washington to the bone, and tried to emulate him in everyway, even i do not see him as taking the Presidency.
After the war he wanted to fade away, which is why he accepted the Washington college position.