That's roughly the premise of several sci-fi short stories and novels I read (and of which I can't name at least one after having read several hundreds of those).
Dark Forest Hypothesis
Doesn't matter. Any intelligent alien species smart enough to interpret radio frequencies could also see the Oxygen and Methane in the atmosphere and figure out there's life.
Additionally, they'd see all the CFCs, and manufactured chemicals we've been dumping into the atmosphere and know there was post-industrial life. The way our sun's light interacts with our atmosphere makes a bigger signpost than any radio broadcast we can make.
We've been announcing our existence to the universe ever since the Great Oxygenation Event, if not before. All they need is a telescope and basic spectroscopy from the chemical signatures of our atmosphere.
https://en.wikipedia.org/wiki/Great_Oxidation_Event
There's a bird in the forest, plain for all to see, if they look. But they're not looking until he starts singing.
(Serious, does that analogy stand up?)
Depends on the alien species: We humans are already looking at other planets and their atmospheres, and we have no hope of going there or making contact with anything even if it exists.
If they are anywhere near as curious and as advanced as humans, they've probably spotted us already. (well, "as advanced as humans", we've only been able to look at other planet atmospheres since like ~2016, when ever certain satelites launched, soo...)
In a sense, yes and no. It's far easier to pick out some very irregular signal (human communication) in a sea of noise (all the spectra coming from every planet orbiting a star) than to randomly recognise that a specific planet has a specific atmospheric composition. At the same time: To pick out that signal, they have to be scanning the part of their sky where the earth is.
To put it this way: Any advanced civilisation that takes a closer look at our specific planet (as we're doing every day with loads of planets) and looks at the absorption spectrum of our atmosphere (like we do) would recognise that there's a high probability of life on our planet. Maybe they could even infer a high probability of "intelligent" life (broadly speaking). On the other hand, any civilisation that looks in our general direction would likely be quick to notice that there's some non-random signal coming from around where we are, and may decide to check it out more closely, eventually homing in on our planet. At that point, they'll likely be quite certain (together with the evidence from our atmosphere) that there is intelligent life on our planet.
Either way, I like the following way of looking at things: The universe is estimated to be around 13 billion years old. The Earth is estimated to be around 6 billion (please arrest me if I'm wrong here, I'm talking off the top of my head). For the first couple billion years, no planets, or at least planets with relatively diverse elemental composition, existed. I see it as not entirely unlikely that we're quite early in developing a space-faring society in the universal sense. There's not that many solar systems with the composition needed to sustain life as we know it that came into existence before ours, so we might just be first.
If that's the case, we might be the civilisation that others are warning each other about in a couple million years.
Sounds like a Chinese proverb.
“Two possibilities exist: either we are alone in the Universe or we are not. Both are equally terrifying.”
― Arthur C. Clarke
How far away can that stuff hypothetically be seen from?
The sun ignited about 4.6 Billion Years ago, so anyone around 4.6 billion light years away (a little more due to expansion of the universe) could see that there are planets orbiting a star that's capable of sustaining life could see it with a big enough telescope.
https://en.wikipedia.org/wiki/Sun
Tectonics and water would have been around on Earth for around that same amount of time, so as soon as the Sun fired up, it was showing the universe that there was a planet with water on it.
https://en.wikipedia.org/wiki/Origin_of_water_on_Earth
The Great Oxidation Event happened around 2.5 billion years ago, so anyone 2.5 billion light years away would be able to see it with a big enough telescope, and know that something interesting happened that suddenly released a bunch of Oxygen.
We've been ramping up technology for 10,000+ years, but really started dumping interesting chemicals into the atmosphere when the industrial revolution started around 250 years ago (so 10,000 - 250 light years away.)
https://en.wikipedia.org/wiki/Industrial_Revolution
We started firing off nukes in the 1940s, so probably the last 80 years we started showing the universe that we're nuclear technological intelligence.
So depending on how far away someone is trying to observe us, they'd be able to see different life stages.
Even in another nearby galaxy, they could see the spectral lines of these signatures if they had our telescopes, and used gravitational lensing. They could even park something like the Hubble Space Telescope a couple hundred AU away from their star and use it as a giant telescope to see us from extremely far distances.
It may not be an intelligent species that the message is warning about. The fear could be of a creature/species that hungers, and has some senses that we don't.
And even then, they would have pretty limited reasons to bother us ahead of schedule. Interstellar space is big, crossing it just to be a dick can't be ruled out, but that's about the only reason anyone would prefer an inhabited planet over a younger, emptier one that's closer.
Nah, that's them warning each other from contacting us.
