Not necessarily, anytime it was on it would update the ddns service with the correct IP address. As far as I’m aware, your dynamic IP doesn’t change too frequently. There would be some downtime if your ISP assigned you a new dynamic IP while the machine was powered down but it would correct itself as soon as the machine came online again.
I’m not an expert but I think this is accurate.
Edit: Does Synology have a ddns app? Or is it possible to install a ddns service via the command line? It would be cool if the NAS could send the update!