If a society was advanced enough to go star hopping through some advanced transportation system and they were curious about their surroundings (like us) AND they were carbon based, oxygen breathing
(like us) they very well might go looking for Planets that were oxygen based
atmosphere, same size as their home planet (within a certain +- factor for gravity) and capable of sustaining their life form.
Already we are starting to look for Earth like planets in the nearer stars that might be capable of being visited and or colonised (should we ever develope the means to get there). A part of it is our curiosity and a part of it is the fact that we know we are capable of being wiped out. But we are looking, even though we can't go yet, and they have alreasy spotted several candidates. They are probably wrong about them, but they have found several earth sized planets. So far most are not in the band where life as we know it is probably possible ( too far from their suns or too close)
But if that species had the tech to get somewhere, they probably would also have the tech to weed out the unlikely candidates. This would include stars with the wrong light spectrum (red giants, binaries, blue (too young), and a zillion other types of systems. When you start applying this weed out process and start selecting down, the number of systems that might work become a lot lower. (There is even speculation that a single Large Moon might be needed to promote life forming). Anyway, it might be that there are only a few million such planets in the entire galaxy, so a very advanced
tech society might decide to check them, or at least the closer ones. Assuming their transport system is FTL (sort of a warp drive so they don't spend years getting there and back) then it becomes possible , maybe even likely, that they may have visited earth at some time in the past (or might in the future.) It is still unlikely that they will be doing so RIGHT NOW, unless they are very far away, or are so advanced that they don't care.
At any rate, the point is that you don't check EVERY star, just the ones with earth sized planets , a certain distance from a G type (yellow) non variable sun that is of the right size and class. Those are the ones we would be checking if we had the means to go.