No. You should read "Hawaiian Antiquities" by David Malo, a Native Hawaiian historian who lived during the early Kingdom. He documents what happened on the mountains, and as far as I can recall, he only mentions Mauna Kea to mention an adze quarry that was used. You can also read Liluokalani's book. She mentions sacred mountains, but it's Mauna Loa, not Mauna kea. That's not to say there hasn't been religious significance but that it never stopped things like rock quarrying or hiking, or even the early telescope building.

This idea of the mountain being tabooed for anything but Native Hawaiian religious practices is a recent invention by the Native Hawaiian sovereignty movement in the form of the TMT protesters, as well as a new "sacred" name they cooked up for it "Mauna a Wakea".