[Question] Can I register an SPN for a SQL Server instance "online"?

tl;dr: Pretty much what it says in the title.

We're currently in the process of moving a number of databases from one instance (default) to another (named). There are a number of people in the bussines (and other systems) that have connection strings to these databases, so to lessen the impact of this move I was following the advice here.

I can now connect to the instance with the old servers' host name, but with windows authentication I get the error caused Kerberos authentication not working as the principal name is incorrect. Can I run setspn online without impacting the stuff currently running on the server?