It's more likely due to eased voltage sag. When any electrical device is put under a load. The voltage supplied will drop until things stabilize again, hence the name voltage sag. If you've ever noticed your lights dim when the air conditioner kicks on, that's voltage sag due to the high startup current demand of the compressor.
In a healthy battery, this sag is minor and not detectable. As a battery ages, the sag becomes more pronounced, to the point you see the meter drop. In extreme cases the sag can fall below the safety cutoff voltage of the battery, which is what causes the sudden shutdown when you think you still have power available.
What I think is happening in safe mode is your battery is charged enough to get past the boot up sequence without the voltage dropping to the cutoff point but does drop enough to affect the battery meter. After the boot is complete and the phone goes to an idle state with minimal background processes running, the battery voltage recovers somewhat. That tricks the battery meter into thinking the battery was charged some.