My uncle has a Private Equity firm. I talked with him about Holacracy a couple of times. I learned two things:
1. On company valuation: His perspective is that in SME firms his valuation depends a lot on the dependency on the founder/director. eg how good will the organization perform if the founder/director leaves after the sale? A high dependency means for him a lower valuation.
Holacracy is a way to make this dependency explicit. and it also makes the dependency less risky. with a role based structure in case the founder/director leaves it can adapt its structure and do transitions role by role - instead of needing to find a copy-cat of the founder to keep the organization running.
2. on investor-company dialogue: Additionally as investor it is sometimes hard to get good information about performance beyond the yearly report and the monthly "meeting room" conversation with the director. A fully transparent way of working helps to make the investor-company relation much more productive.
its just a story. I dont have an actual case.
I know that Springest here in the Netherlands just finished an investment round. No idea how running Holacracy played a role in that.