Yes, but also no... There are about 4x10^11 stars in the Milky Way galaxy, which from an exploration standpoint is massive. But 10^11 isn't exactly an inconceivably large number... let's suppose for the sake of argument that the development of complex multicellular life capable of creating and using radios is 'gated' by only two independent one in a million chances per star.. that's already 1 in 10^12. For 4x10^11 stars in a galaxy, that would mean the galaxy has a 2/3rds chance of not having even one star system with radio-capable life.
(1 - 1/10^12) ^ (4x10^11) = 0.67
My favorite "crazy theory" is that the Paleocene–Eocene Thermal Maximum (PETM) was caused by a previous industrial civilization that, like us, found a bunch of easy to access hydrocarbons, naively dug them up and reached the same climate change problem that we did, ultimately wiping them out.
Of course there is 0 evidence for this at all, but it was also more than 50 million years ago. If you look into it basically nothing about an advanced industrial civilization would likely survive to make it into the geological record for us to observe. The only reason to even entertain this hypothesis is that the PETM also experience a very rapid increase in atmospheric CO2 and we aren't entirely sure why.
Unfortunately this means that there's probably not much chance for a rich field of xenoarchaeology to exist since it's not even possible to do this on our own planet.
What is an interesting thought experiment is: Suppose we realized we as a civilization were doomed and wanted to sent a message to future industrial civilization on Earth warning them about being too aggressive with hydrocarbon usage. To my knowledge there is no known method to ensure a message could be sent that far in the future, but it's fun to try to think of ways we could send a message to a future, essentially, alien civilization here on Earth.
There also don't appear to have been any spikes in atmospheric carbon dioxide during the relevant period: https://en.wikipedia.org/wiki/Carbon_dioxide_in_Earth%27s_at...
Though maybe you were looking at a data source with better resolution?
https://www.scientificamerican.com/article/could-an-industri...
I think you've reached this statement too eagerly but would be interested to discuss this point. Do you mean that the materials they used would have disintegrated and their (presumably carbon-based lifeform) bodies wouldn't have left any fossils?
My main thoughts on this come from reading Vernor Vinge's [1] excellent Marooned in Realtime which discusses some of the condundrums resulting from transferring information over massive periods of time. I think part of it talks about subduction zones where everything is eventually riven back into the Earth's mantle, essentially lost to any kind of current archaelogical techniques.
Paradoxically, extending on your thought - I guess anywhere with living conditions similar to earth (oxygen atmosphere, water, weather, etc) would not be conducive to long term archival of civilization artifacts.
So you'd have to look at 'dead' places if you want to find evidence of civilization. Or stumble across an derelict megastructure (dyson sphere\niven ring\etc)
If there's been on average a thousand civs spread across the Milky Way for the past 5 billion years, then we need something else to explain why none of them have colonized the galaxy.
"That said, the results indicate that the probability we are alone (<1) in the galaxy is significant, while the maximum number of contemporary civilizations might be as few as a thousand."
A thousand civs spread across a galaxy means there is a low probability of meeting live aliens, but does that mean xenoarchaeology could be a thing?