Short answer = not really.
While a regulated mod will keep a battery from being overdischarged down to a low voltage, if the protection electronics are working properly, the mod has no idea what the current rating of the battery is or its condition.
Some mods measure temperature and shut down when hot but that’s just the temperature of one part of the regulator circuit board. It has nothing to do with the battery. A battery with too low a current rating for the way you vape could be run at way beyond its rating and the mod would have no idea that it’s happening. The mod can only act if the battery’s voltage drops too low.
A lot of regulated mods don’t even have fuses that can blow in order to disconnect the battery in case the mod’s electronics fail and the battery is being short-circuited.
Lastly, if there is damage to the wrap at the top of the battery you can short-circuit the battery when it’s inserted or removed from the mod. Even wrap damage on the side of the batteries can cause problems. If the metal cans of two batteries in a series-connected mod touch then one of the batteries will be short-circuited and could vent or burst. No circuitry in the mod will protect you from this.
So while a regulated mod can help protect us from short-circuits in the atomizer, and batteries that are nearing empty, mods will only protect themselves for any other problems. We still need to choose batteries with a high enough current rating for the way we vape and be vigilant about the condition of the wraps and top ring insulators of our batteries.