In my opinion yes, in my opinion 18 years of hype did damage in relation to peoples expectations for Shenmue III, I think i finished Shenmue II for the first time in 2017 so i didn't wait a lot of time for Shenmue III, i didn't imagined that Shenmue III needed to be like Shenmue II to be good, nothing like that.
But i can imagine how painful it was to wait 18 years for the saga to continue, 18 years just imagining Shenmue III, making theories and much more, this was hard for many people.
For 18 years a lot of people imagined the perfect continuation of Shenmue II, 18 years of hype did damage in my opinion because after 18 years the hype was so high, the expectations was so high that people wanted a lot of things.
Probably people wanted to see Ziming and the other leaders, Xiuying returning and all the things and theories they imagined for 18 years but this didn't happen so it was a deception for them, but i feel that this will happen in Shenmue IV, Shenmue III is about other things.
I can understand this feeling of wanting more things but Shenmue is a slow pace story in my opinion. If Shenmue III was released at that time then i think people would received the game better, one of the reasons is waiting less for a continuation so less hype, people waited for 18 years so the hype was high, and Shenmue III was a kickstarter game, Yu Suzuki was not with SEGA anymore, it is sad but it is what it is.
But i disagree when people say that Shenmue III did not advanced the plot, that Shenmue III only have 20 minutes of story and things like that. Shenmue III is about other things, Shenmue III to me is about Ryo living with Shenhua in Bailu village like second home to him, is about Ryo and Shenhua getting to know each other more and living together, it is about developing their bond, it is about the peaceful and calm time in Ryo's journey, it is about Ryo training and developing more as a martial artists and much more.
My final answer is yes, Shenmue III would be received better if it was released in 2003 or 2004 for example, people imagined this game for 18 years and expected too much, the hype was really high but of course that people can dislike the game and that's okay, but i really feel that the game would have been better recieved at that time.