Someone else can figure out the math, but I'm pretty sure the energy from all of the nukes that have been detonated, especially if you only count the open-air ones, is minuscule compared to what the sun gives off. That would mask any possible detection. I wouldn't be surprised if just the solar radiation that the earth reflects is enough to mask the nuclear blasts, unless you're viewing them from right inside the solar system.

The spectral signature would be quite different.

In Pellegrino and Zebrowski's The Killing Star, it's the know-it-all attitude in Star Trek that seals our fate.

What kind of unique signs would a nuclear explosion create? Doesn't nuclear fission occur naturally?

Not really? Only in very rare exceptions. At least if you're talking about chain reaction fission.

Those gamma-ray bursts have to be coming from somewhere, I guess.

Gamma ray bursts are from interplanetary war? That's a terrifying thought.

My pet conjecture has always been that they're the interstellar equivalent of "Hold my beer and watch this..."