We are going to enable Kerberos to allow double hop authentication between our SQL Servers. Our company is nearly 24 hours which leaves a very small window for server restarts. Is it possible to enable Kerberos without requiring a reboot of our Domain Controllers or our SQL servers?
Kerberos is already enabled, it's how active directory works, what I assume your talking about is enabling delegation from your web server(or other application server) to your SQL server, this does not require a reboot.
That said, as pboin mentioned, I would always try this in a test environment first.