He will next appear on August 10 to enter a plea.
A maximum penalty for the charge is 14 years imprisonment.
Storer's England-based family have been granted a border exemption by Immigration New Zealand to visit him in hospital.
They will still need to provide negative test results and book a spot in MIQ before entering the country.
Givealittle and GoFundMe pages were set up by friends and the pub owner after the incident to help cover the cost of travel for the family.
The 25-year-old's parents Ian and Dawn said a friend held a phone to their son's ear at his hospital bed so they could tell him the news.
They have been told by doctors via Zoom there are three scenarios for Storer's future.
"One, he won't survive," his father said.
"Two, he could survive but with damage. And three, he could survive and almost return, maybe, to normal."
Storer has been described by friends as "a good bloke" who loved fishing and the pub.
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