Let's go with the first option of it accidentally getting absorbed - I think potentially she could have chosen it on her own eventually if it seemed like they didn't have the information they needed and times were dire/desperate. But I like playing with that aspect of herself that struggles to disobey magical commands still due to the way she was created despite how far she's come and how much she resisted with Wangji's help on the way to get this to begin with (Thanks for the help, Wangji. You're a real one.) Then to follow the compulsion to peer into well, to grab, and to drink after using all that willpower to get there and not hop off into the water along the way.

So yes, she will absorb and see all the memories and it will be a lot, but the Matthias one will be important to know.