Can a venture fund invest in a company organized as an LLC

VCs don't invest in LLCs.
LLCs are pass through vehicles and issue K1s to all members, so all gains and losses are passed through to the fund, and the fund must pass them through to every LP.
In addition to the MASSIVE accounting and tax headache, if a company is profitable and they don’t distribute dividends, VCs will need to report taxable income to their LPs.