She had roughly six months of consciousness in which she swam through the lifetimes and memories of a huge number of her ancestors with nobody to speak to except them and her mother through a quasi-telepathic link.

The link is actually more temporal than telepathic as i understand it because both Reverend Mother Gaius Mohaim and Alia both deny telepathy but the line is "She is in my mind where she should not be." She also shortly after describes to Paul that she is sending him a message by "writing it on the future stream of time for [him] to find."

So she wasn't a mentat, but was basically born as a fully realized Bene Gesserit Reverend Mother which includes incredible mental discipline alongside Prana Bindu techniques; while not capable of the phenomenal computations a Mentat is, they can still assimilate and process bare scraps of information into complete pictures significantly quicker than the average homo sapien.

I finished reading the first book again only yesterday, so this is wildly fresh to me.