Powering a MCU from a battery without a regulator
If your battery voltage drops to a value between 0-1.7 it isn't defined what will happen


This is often true, but it won't, for sure, destroy anything. Because, if it was destructive, the min Vdd in "Absolute Maximum Ratings" would have been given as a positive value (which I have never seen in any datasheet, and I hope I'll never see that in my life - it wouldn't make sense).

So at this point, you are guaranteed the MCU won't be destroyed with undervoltage. However, it could still behave erratically (potentially damaging other external circuitry).

Now, in this kind of MCU, there is often a feature called "brown-out detection", or, sometimes, "undervoltage lockout". This is a feature that monitors the supply voltage and guarantees that the chip is held in reset state when the voltage is under a given level (sometimes programmable).

Good news: There is such a feature on the specific chip you're using. See chapter 5.1 in the datasheet you linked.

Therefore, you don't need to have a regulator with "power good" detection or an additional supply monitor circuit in your specific case.

Note that, if the MCU didn't have the brown-out detection included, there are tiny chips that just offer this feature (often combined with a timed power-on reset generator) without being voltage regulators.