poll of transfem people taking Progesterone regarding sex drive:
https://octodon.social/@siege/110441708843689395
testosterone is not the only hormone that influences sex drive - estrogen certainly does, theres no reason to assume progesterone doesnt except ongoing association that women dont naturally have sex drives / sex is a masculine urge.
How quickly youll feel any effect definitely depends on how you're taking it. Orally you'll notice some effects within half an hour since its metabolites act as a sedative. However that will be nullified if you're taking a blocker like finasteride (that will prevent the prog from breaking down to allo).