Would what Oswald did have made sense if the CIA were under the control of the KGB?
The CIA was under the control of the KGB in the sense that the father-figure-requiring Chief of Counterintelligence, James Angleton, was manipulated by a probable KGB "mole" (Bruce Leonard Solie) who was aided by other probable KGB "moles" (e.g., George Kisevalter).
What did Oswald do?
He starts teaching himself Russian while still in the Marines.
He gets out of active duty several months early.
He goes to Moscow.
He walks into the American Embassy and tells the probably-expecting-him Consul (and probable CIA agent) Snyder and the KGB's hidden microphones that he's going to tell the Soviets about Marine Corps radar and what he knows about the U-2.
He lives two blocks from a KGB school in Minsk for two-plus years.
He marries a former KGB "swallow" and probable KGB informant.
He returns to the U.S. with his wife and young daughter.
He starts his own chapter of the Fair Play for Cuba Committee.
With or without encouragement or logistical support of the KGB, he tries to kill Edwin Walker.
He tries to visit Cuba and ostensibly move back to the USSR.
With or without the encouragement or logistical support of the KGB, he kills JFK.