Just watch an ATC delay you after you've declared minimum fuel...............don't think so
I've seen it where they don't give priority to aircraft until there is the imminent threat of a PAN, and even then it was a case of asking other holding aircraft to volunteer to have their slot time adjusted to accommodate the min fuel call aircraft. He was moved up in the sequence to a landing time that just avoid the PAN by a few minutes.
I would NOT be hanging my hat on getting any priority whatsoever with a min fuel call. If you do that's a bonus, but not to work on as a plan and assume it will "just happen".