Listening to your recovery feed could also have a potential impact on a network level. As pjz mentioned, your NIC and IP stack will have more frames/packets to process. In addition, more of your available bandwidth is being used up by data that is not being used by your application; this could lead to dropped frames if there is congestion on your link. Whether congestion is likely to occur depends on whether your server is 100Mb or 1Gb attached, how much other traffic your host is sending/receiving, etc.
Another potential concern is the impact on other hosts. If the switch your host is attached to does not have IGMP snooping enabled, then all hosts on the same VLAN will receive the additional multicast traffic, which could lead them to experience the same problems as mentioned above.
If you have a networking team administering your network for you, it may be worth seeking out some recommendations from them? If you feel it is necessary to subscribe to a redundant feed, it would seem prudent to work out what level of redundancy already exists in your network and how likely it is that messages on the primary feed will be lost.