Yes, but does God care? I think not as they still reject the sacrifice of His Son. OT sacrifice was a type that points to the true sacrificial sacrifice.
But it is interesting. Possible Divine Rejection may occur.
I think He cares.
What’s fascinating about this storyline is that all those Preterists who will die on their hill insisting that there will be “no more Temples built” and that we’re somehow right now living in the “Millennium Kingdom” of Christ (make that two millenniums), will have a hard time negating that this Red Heifer story and the New Temple projected to be built actually shatters their version of events since a decent portion of Orthodox believing Jews are actually working towards these goals.
Jews still have another “seven” to complete for Daniels Prophecy. That is exactly why this story is so important.