No way. Gallo had been affiliated with the Profaci family, predecessor of the Columbo family, but he and his brothers split with Profaci and declared war on him ca. 1960, over a dispute involving territories promised by Profaci, who then welshed. Joey went to prison for a long stretch in the '60's. When he got out, he made demands on Columbo going back to Profaci's welshed promises, but Columbo refused.

At the time of his death, Gallo was making a career of being a public figure, giving interviews to magazines, pretenting to be an "intellectual," and being a chi-chi pal of the rich and famous. Probably had no connection with crime--organized or otherwise.