Here at Small Devices, we've been amazed at the improvements we got by adding the MI:Power Board to our BBC micro:bits. One of the first questions was, "Is it safe to charge the micro:bit while the battery is connected..to which I answered, "probably...well, as long the the battery isn't getting hot..". However, to make sure, we did go and look for a diode that would protect our 3volt CR2032 watch battery from inadvertently charging when the micro:bit is plugged into USB on a computer.
So the answer is "yes, it is safe to plug the micro:bit into power when the PI:Power Board is connected". As you can see in the included Kitronik video, the board also adds a power switch so you can leave the battery in without it draining; then plug it into external power to save battery if you're coding for an extended time.
Since it's possible to also code for the micro:bit in lower level code such as C or assembly language, as an advanced exercise you could also modify code to minimise use of power.