Weather radar energy isn't particularly hot. I know a bloke who was leaning against the radome of a jet, chatting to an engineer, after a while his arm got a bit of a tingling feeling. On return to the cockpit he discovered the radar was transmitting! So leaning against the actual radome with it transmitting he got a slight tingling sensation after some time. Any birds far enough away to have not already noticed the big noisy chunk of metal coming their way aren't going to feel a thing from the radar.