What happens when an SSL certificate is cancelled?

Putting aside the fact you have 300 servers (!!!) and you seem to say the process is not automated so it will take 10 days (!!!) to complete, the scenario that GoDaddy has described seems off. NOTE: Comment irrelevant now that a clearer context is placed on the 300 servers in 10 days issue; the logistics of moving/sporadically-connected servers make sense.

Yes, if you wish to create a new certificate the old SSL certificate should be revoked (aka: cancelled). But in my experience SSL certificates don’t have to immediately be revoked because a new SSL certificate has been issued. You might want to double check with GoDaddy about this.

Also, SSL certificates, registrars and hosting services are 3 different things. Sometimes a registrar will insist they are the only ones who can issue an SSL certificate for a domain they might have registered with them. But you can pretty much get an SSL certificate from anyone who offers one and then use that with your current servers without issue.

If GoDaddy is really being a pain about this, I would recommend just getting an SSL certificate from another source.

That way you can phase in the new SSL certificate across the 300 servers while keeping the old SSL certificate in place. And then when you are done with the transition, officially revoked the old certificate so you're done with it.