An absorbent glass mat (AGM) type battery would not work, for long, if installed in a Tesla vehicle. The charging requirements of an AGM battery are different than what is required for a conventional flooded lead-acid battery. The charging voltage starts out higher in an AGM battery but then the float voltage (the voltage to maintain the battery once it has been charged) is almost a full volt lower for a 12V AGM battery, typically 13.5V to 13.8V depending on the temperature. The float voltage of a conventional lead-acid battery is ~14.4V.
If you take a voltage reading from the Tesla's 12V accessory port, it is 14.4V. This would result in an overcharge of an AGM battery, shorten the life of the battery. That is one clue to the fact that Tesla does not use an AGM battery in their vehicles. A second clue is that the 12V is installed under the hood of what would be the engine compartment if the Tesla vehicle had an engine. AGM batteries can be installed under the hood as well but they are just as likely to be located inside the passenger compartment, i.e. underneath a rear seat or under the floor of the hatch or trunk.
Automotive designers are free to place an AGM battery in any orientation in almost any location in a vehicle. The same placement flexibility does not exist for a conventional flooded lead-acid battery. If a conventional battery case ruptures due to a collision or a battery fire/explosion then the electrolyte, concentrated sulfuric acid, would be released. If the same was to happen with an AGM battery then at most just a small amount of electrolyte could leak as the electrolyte is held in the fiberglass mat like a damp sponge.
Tesla could have chosen to use an AGM type 12V battery in their vehicles. AGM batteries cost more than a conventional battery.