I am not a scientist or a doctor, so I can't give a yes or no answer, but can lead you to places where I found a LOT of information about the subject. Here is some information I found, and where to read it for yourself.
With that being said, I still use caution when feeding the birds. If you do find a dead bird, contact your local government agency, here is a map through the CDC http://www.cdc.gov/ncidod/dvbid/westnile/city_states.htm, call the hotline on the above map for procedures.
According to the sites I've read, the best defense against West Niles it to use a good mosquito repellant, and remove standing water to reduce the mosquito population in your backyard. There are also products on the market to kill mosquito larvae in standing water, like Mosquito Dunks and Mosquito Larvae Killer, which uses natural garlic to kill mosquito larvae and it also works to repell mosquitoes from your backyard.
To help the birds from infections and disease, routinely wash your bird feeders with a 10% bleach solution and allow it to thoroughly dry prior to refilling the feeder. Use gloves when cleaning your feeders to protect yourself from anything that may be on the feeder as well as the cleaning solution.