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You can get from the border in South Texas (McAllen, TX supercharger) to Puebla on superchargers only. But then you have a 930+ mile stretch from the supercharger outside Puebla to the supercharger in Cancun with no fast charging options available. There are hotels with Tesla destination chargers over that drive though, so it's possible to make it on the L2 chargers. However, many of those destination charger locations require you to be a guest of the property in order to charge.
So, the straight answer is that yes, it's possible to drive to Cancun in a Tesla. But it's still only feasible for those who are okay with a slow and somewhat adventurous trip and who don't care about having freedom of choice in their itinerary or lodgings for a significant stretch. However, this will be changing in the not too distant future. Tesla has plans for new superchargers in Cordoba (maybe 2022) and Minatitlan (maybe 2022) in Veracruz state as well as in Merida (Q4 2021) and Valladolid (Q4 2021) in Yucatan state. With those locations activated, you would likely only have a single forced overnight on destination charging L2 at a hotel in either Ciudad del Carmen or Campeche.