""Looking at the Command Reference guide, it talks about local pools and PPP connections. With this in mind, I am wondering whether this command only works with PPP connections. Hence my confusion.""
No, gratuitous arp works with many failover situations and not just PPP, HSRP is one of them.
""If we deploy the 'no ip gratuitous-arps' command, as noted in security recommendations, will this stop the switches from updating the change of MAC address to virtual IP address when we have a NIC failover? Therefore breaking the failover process""
As per the CLI description "gratuitous-arps Generate gratuitous ARPs for PPP/SLIP peer addresses" it should only disable the switch/router from generating gratuitous ARPs. However, I believe the switch should still flush out the ARP entry when it receives a gratuitous ARP message from the server itself.
HTH
Sundar