hmmm, I think that could make sense, but there are some things that may point to that not being the case.
Like how Rachel took the report of the three girls (Catherine, Mika, and Chloe) seriously.
Now yes, there is nothing saying she wouldn’t take the reports seriously, but she knows Catherine is a part of the 4 Founding Families, even if she was playing things smart, just like Catherine is to Hannah, she would hold a grudge with Catherine just for being associated with the families.
another thing that would tell me that that may not be the case, is how the head mistress of Foundsbouroh talks about Rachel. Simply put, Rachel isn’t very smart, well, at least not at the top of her class. What am I getting at? In that regard, it’s safe to say that Rachel wouldn’t be able to come up with an elaborate enough plan to reform the founding families, unless she was REALLYYYYY playing the long game this whole time, which we can doubt.