Super cool and intriguing idea, but we would probably never see it. A nuclear war on another planet would give off a short flash of light in UV and infrared, but it wouldn’t last long - maybe just a few hours. We should be looking at the right planet at the exact right time with the right kind of telescope. Super unlikely. Even then, it might just look like a random flare from a star. So yeah, maybe it's possible... but we would almost definitely miss it.