No not possible - endo is exactly the same cells that are in the womb - they don't know they are not in the womb. So they will respond in the exact same way the the lining of the womb is responding right now.
If you have a period - so too does the endo wherever it may be.
If you are pregnant and the lining of the womb in thickening as the embryo implants ..same thing will happen to the endo lesions, they will thicken too and stay put till the end of the pregnancy.
Having a cyst and having a pregnancy with an expanding uterus will inevitably push the cyst out of the way ...and probably land it right on the bladder for the time being so when the bladder is full the cyst is heaved up again and can cause pains.
However the main reason for pains that may feel like endo pain are adhesions or sticky scar tissue sticking organs together. They are as tough as superglue, but as the organs are supposed to be freely moving around and able to move as the expanding baby/uterus pushes them out the way, if they are stuck with adhesions then these have to stretch and snap or tear where they are anchored and this will be painful in the early stages of pregnancy, if they were not cut in the weeks before getting pregnant during a lap op.
It doesn't last the entire pregnancy because once they are snapped or torn to allow your organs to shift about they should be prevented from resticking by the ever expanding baby.
So what you think are endo pains and probably are adhesion pains will eventually stop as everthing that does need separating will have separated.