The answer to your question is No and Yes.
Most electrologists practice in such a way that they would only effect permanent removal on anagen hairs only. Hairs in other phases would be weakened, but would return thinner and weaker later. At that time they can be killed for good with a lower treatment energy.
There is a process that has shown that hairs in any phase can be treated, but since it is more painful, very few electrologists outside of Japan practice it.
So although there is a way to do it, most US and UK electrologists don’t practice it, and if you are getting full clearances anyway, there is no need to do it because you will look finished while catching up with the other hairs as they come in. An electrologist can treat hairs you can’t even see yet. This is especially true of those who have better vision equipment than a simple circle lamp.