On the contrary.
Rei is not necessary to start or create instrumentality.
If you watch EOE, you can see only the mp evas, Shinji, EVA01 and the Lance of Longinus was used to start it.
Rei is not presented as the facilitator at all, but the denier of instrumentality. Rei breaks into the process to save Shinji, and she convinces him to end it.
Rei is in the thick of it because she needs to have the power to get to Shinji. So she assimilated the MP-EVAs and took over their role, making them kill themselves so she remains in control.
The ending of instrumentality is only possible because Rei managed to get Shinji out of his funk, and after it is done, Rei can discard the instrumentality body and return to being godlike.
The character that is left representing inatrumentality is Asuka, and there is direct dialogue accusing Shinji of using her as an escape. Not for Rei.