O'Brien has never been to the Academy, and he once said he was offered an officer's commission, which he declined. If it's possible for a Chief Petty Officer to become an officer without Academy training, it would definitely be possible for a Warrant Officer.Can they become full officers that way though? That does seem doubtful, or is there evidence to the contrary?
Besides, attending Starfleet Academy isn't even the only way to become an officer. Michael Burnham never attended the Academy and she joined Starfleet as an officer.