Можно ли использовать Cisco IOS NAT с протоколом маршрутизатора с горячим резервированием? (HSRP) для предоставления резервных ссылок на интернет-провайдера?

Да. NAT does provide HSRP redundant. Однако, it is different from SNAT (Stateful NAT). NAT with HSRP is a stateless system. The current session is not maintained when failure takes place. During static NAT configuration (when a packet does not match any STATIC rule configuration), the packet is sent through without any translation.