It depends. Most transactions of that scale would be structured to avoid the requirement of making a '33 Act or '34 Act filing although some exemptions do require a bare bones minimal notice of the claim of exemption to be filed with the SEC and state officials.
Generally speaking, the '33 Act applies to all "public offerings" of stock that are not exempt from registration (a tricky topic discussed below).
The '34 Act requires public disclosures to be made by: (1) all banks with 1,200 or more shareholders, (2) all other kinds of companies with 500 or more shareholders, and (3) all other kinds of companies with 300-499 shareholders which have $10 million or more in total assets in any of its last three fiscal years. Disclosure starts automatically following a '33 Act offering until the '34 Act threshold is no longer met, and also applies in cases where the '34 Act filing requirement arises in the absence of a public offering subject to registration under the '33 Act.
But, a great many offerings of stock are exempt from disclosure and constitute "private offerings". The safe harbors to qualify as a private offering are mostly set forth in SEC Regulation D, 17 C.F.R. §230.501-508. Various combinations of other exemptions exist involving some mix of a limited number of investors who are not "accredited investors" and a limited dollar amount.
Essentially all offerings of less than $1 million are exempt from federal registration although they may be subject to state "blue sky laws" under Rule 504 of Regulation D.
The transaction you describe, in which all sales of stock that are limited to accredited investors (of which Hedge Funds would be an example), regardless of the dollar amount of the transaction, are exempt from '33 Act regulation under Rule 506 of Regulation D. Some of the California specific details are described here, but basically, state regulations is coordinated with federal regulation in this area.
There is also an "intrastate offering" exemption from the '33 Act, but it is generally very narrowly defined in light of the expansive reading that has been given to the Congressional power to regulate interstate commerce.
If there are sufficiently few total shareholders in the venture (i.e. fewer than 300), it is also exempt from '34 Act filings as well.