I have experimented with the myth over thirty-something years, and found that it doesn't make a jot of difference to the birds whether the radar be turned ON or OFF.
I believe that the origins of birds aversity to radar goes back to WWII when birds nesting on the (stationary) very high energy RDF transmitters in Eastern England were promptly microwaved on the spot. A bit hard for them to nest on the later rotating ground radar transmitters.
Every myth has it's origins, maybe this is one of them, maybe it's not...............
Regards,
Old Smokey