It is possible and exceptionally rare, and you should not book a standard Peninsula cruise hoping for it. Emperor penguins do not breed at the landing sites those cruises visit. An emperor seen on a normal western Peninsula route is a straggler, a long way from anywhere it should be.
Exceptionally rare is the honest label. Some guides have seen a handful of unexpected individuals over their careers. Others have worked ten years and never seen one.
If emperors are genuinely the reason you want to go, that is a different product. A dedicated emperor expedition targets a known colony, usually through a Weddell Sea or Snow Hill Island operation, and it typically involves an ice-capable ship, helicopters, long walks and a narrow operating window.
Dedicated does not mean guaranteed. Ice, wind, visibility and flying conditions can stop you reaching the colony even after the ship gets to the region. Ask any operator selling one what happens if the ice does not cooperate.
People ask us for the best week to catch a stray emperor on the Peninsula. There isn't one. Our own guides have noticed occasional encounters in late October and early November, but that is a handful of anecdotes, not a pattern. Nobody should choose a departure date on the back of it.