Not too sure about probability and all the philosophical stuff that people tack onto it, but the simultaneous occurrence of oxygenation of planets seems high unlikely, at least on a small scale like a single galaxy.
If they have their own technology, whatever that is, they most likely will not pick it up. Maybe they pick it up, and completely dismiss it as noise. They could be sending very weak signals to us, but we have not been able to pick it up with our technology.
But radars, whatever they may look like, are built to detect stuff. Signals are light beams and I'm pretty sure that if they got radars up, they can detect all across the electromagnetic spectrum.
They might not see in visible light though, which could be interesting. Imagine if they saw in infrared! We would be glowing figures to them, since we radiate energy in the infrared part of the spectrum. 8D
Who knows what evolution is capable of? In fact, they recently discovered a species on Earth that does not need oxygen to survive. It was once thought that only bacteria could survive without oxygen.
New species 'lives without oxygen' - Telegraph
That single cyanobacteria evolved into other stuff like these. Evolution does wonders.
Biologically, respiration is the only known way to produce enough energy to support large multi-cellular animals, i.e. intelligent life. But biology only describes I guess.
You might to read the comments. It seems they still haven't figured out how the organism functions without oxygen, if it does at all. One commenter suggested the possibility of it working like jellyfish.
Annnnnd >.< Cyanobacteria were the first known protists with photosynthetic organelles and were the ancestors to plants. It's speculated that they were responsible for oxygenating the primordial earth.
You assumed that they had the technology of radars that are the same concept of radar as us. We can't detect stuff if you go far enough to the electromagnetic spectrum combined with if the signal is weak enough. (Or the tool isn't designed for certain part of the electromagnetic spectrum) We have technology to jam radars so it can't detect stuff as well.
How many years till the sun burns out and goes nova?