I haven't done it with budgies, but I can tell you that the white on a cockatiel glows when you shine a black light on them. The cockatiels aren't very happy about it.
Nothing happens that we can see when you shine a full spectrum light on birds in the daytime at least - I haven't tried it at night. These lights provide UV but have all the other frequencies too, and it just looks like daylight to us. But birds can actually see into the near ultraviolet, and they'll experience colors that we can't even imagine. I don't know whether cockatiels have any markings that show up in UVA light but budgies definitely do.
A black light has a much narrower frequency range which probably helps with the special effects, although you still don't see as much as a bird would. There are some cheap black lights on Amazon for about $7 if you just want to have fun looking at budgies under a black light. If you want an actual full spectrum light to help regulate their metabolism and provide other benefits, I've got a big article about it at
http://www.littlefeatheredbuddies.com/i ... hting.html