There are some hedge funds that invest in startups, along with the investment arm of other companies (Microsoft bought 1.6% of Facebook pre-IPO), but I don't know if it'll work for mutual funds. Hedge funds and companies can sit on a startup for years before getting any return, but mutual funds have to be much more liquid. It could work as a closed-end fund, but those are much less common than open-ended funds and you lose the ability to reinvest in the startups.

http://lxventures.com is a Vancouver based public company that does something very similar to what you just described. It is a very new concept, and hotly debated.

"LX Ventures is a publicly-traded startup technology incubator that launches, acquires and integrates silicon valley style early-stage, high-growth technology companies. "