Not the Yucatan as far as I know (?) but there are some liveaboards that operate in the Caribbean in nearby Central America (Belize, Honduras/Roatan) and islands in the Greater Antilles (Cuba, Cayman, St. Croix) and in the Lesser Antilles (Saba/St. Kitts).
It's possible that the strong currents around the Yucatan aren't the best option for LOBs - I'm just speculating, I don't know. I have been on LOBs that were mostly drift dives from small boats (Sea of Cortez, Red Sea) but most of the Caribbean LOBs we've been on offer diving from the mother ship on permanent moorings, and the same is generally true for Florida and the Bahamian LOBs in my experience. Although that may not be correct for Cuba (?) because I've never done a Cuban LOB trip.