I can't say whether that's a good frequency to use, but I'm certain there are frequencies where the Earth would be brighter at 50 light years than the sun at 1 A.U. But even if there weren't, you could still pick out the Earth.
The two-sided coin is that you have to pick the right frequencies to see the signal in the first place. That introduces the difficulty of looking at millions of channels simultaneously, but it also allows you to rule out natural sources. A natural source will cover a very broad band, so many contiguous channels will be active simultaneously. The sun will look nothing like the Earth.
Finding such a signal is not like trying to find a needle in a haystack; it's more like trying to find a needle in a swimming pool full of pudding. The odds may be small that you find it in any given mouthful, but in the right mouthful its presence will be unmistakable.
Love this. I am going to use it myself with your permission! :)
FTL travel would be great, but outside of science fiction I have not seen it.