Nope, anybody with the Tor browser can.
The only loss here is for the Nazis. The site is now harder to access, harder to find, and to boot now it's open season to go and try to hack the site. Tor protects the identity of the user, so now any random hacker wannabe can go and try their skills against the site without much of a risk of being found out.
The same anonymity means it's also far harder for the Daily Stormer from banning people from the site -- unless they want to make it really hard to access, like requiring referrals. So this development also makes it very possible to simply troll and spam the site into oblivion.