Yes, within about 30 minutes. They are basically useless for theft prevention as a result. Apple nerfed the functionality after someone used it for stalking. You'll notice there is no mention of theft prevention in the marketing materials anymore.

Apple even provide a handy Android app for locating them.

https://play.google.com/store/apps/details?id=com.apple.trac...

You get a notification when an AirTag is following you for some time, but the AirTags owner is not near it. It's meant to detect someone slipping an AirTag on you without the false alarms from, say, taking a walk with a friend who has one in their backpack.

Yeah, I forget the wording but there’s a notification like “so-and-so’s AirTag is near you and they can see where you are.” My spouse put AirTags in our baby stuff and I get them whenever I’m using it.

We have AirTags registered to my wife's account because I use Android. I have one in my work backpack, and every morning I get a notification that an unknown tracker is following me. I wish there was a way to silence the warning for that specific tag.

If an unrecognized AirTag is following you, you'll get a notice.

I'm not constantly notified that my keys are with me. But if you stuck an AirTag in my backpack, my phone would tell me.

No, only if an airtag that's not theirs follows them for an amount of time

Not sure about on iPhone but Android definitely alerts you if an unknown airtag follows you while moving.