Reminds me of a Mythbusters where they wanted to see if turning on and off lights used more power. It only spiked the power for 1/10 a second and during that time it only used something like 50% more power.
So yeah if you used regular light bulbs I guess it could but if you used leds I don't think it'd be a problem. Also at boot up it's not like your video card is running in 3d mode so your psu is probably not running near capacity.
So if you're using regular light bulbs and no video card (or somehow magically put your 3d card into 3d mode at boot up) and running at capacity for your psu then you've got a problem.