While Snopes can't say one way or the other, they do provide some interesting background:
You Bet Your Life was the program that provided Groucho Marx with a career apart from his brothers and introduced him to a generation too young to remember him from his stage or film work. The interview-quiz show, featuring the famous $100 bonus paid to any contestant who said the "secret word," debuted on radio in 1947, aired on both radio and television beginning in 1950, and continued on TV only from 1956 through 1961 — all in all, an amazing fourteen-year run for a quiz show with a tiny budget, a plain set, and a small jackpot (even by 1950s standards).
Although You Bet Your Life was structured to make it appear as though every show were ad-libbed by Groucho, who issued a steady stream of impromptu questions, off-the-cuff remarks, and cutting put-downs to contestants he had met only moments earlier, a great deal of preparation went into each episode. Contestants were selected and interviewed well in advance, and scripts for each week's show were prepared by writers and reviewed by Groucho, who used a crude version of a teleprompter to read his lines during filming (although it was true that Groucho didn't actually meet the contestants until they walked on-stage). However, Groucho certainly had plenty of latitude to depart from the prepared gags and questions (as did the contestants), with the result that much of the conversation was indeed improvised on the spot. About a hour's worth of material was recorded for each half hour program so that flubs, uninteresting segments, and any potentially offensive remarks by Groucho could be edited out.
If you're not familiar with the remark, the Snopes article will tell you all about it.
