If a particle of unknown intrinsic parity decays into 2 particles each with negative intrinsic parity, does that necessarily imply that the original particle also has negative parity?
No, actually it implies that the original particle has positive parity. That's because parity is a multiplicative quantum number, which means that when you want to find the overall parity of a system that consists of multiple parts, you multiply the parities of the individual parts. If you have two decay products each with parity -1, then you multiply them together and get an overall parity of +1.
Of course this all assumes that you're talking about a decay where parity is conserved. Otherwise, the parity of the products doesn't necessarily imply anything in a single case.