Yes and no? The stages exist, but they’re way messier than lists make them seem.
If there is any “stage” that everyone has to go through is the dark night of the soul. That and an initial awakening. I don’t see how anyone could ever get anywhere near union without those two things. The dark night stage pushes you to confront childhood wounds and past traumas. Basically, anything blocking unconditional love gets dragged to the surface. The pain drives you to look for answers, to try and understand why it hurts so much.
The runner usually experiences the dark night differently. For the chaser it’s immediate, but for the runner it’s like something chasing them in the shadows, waiting to catch up but you both go through it.
The awakening stage usually follows the dark night. You start connecting with your higher self, living more authentically, seeing the world differently. A lot of people say they only really discovered twin flame teachings because the pain pushed them to search for answers in the first place.