Can I do anything useful with these tracking bracelets?

So far the only known use for them is to drop them in a location so you can easily backtrack to that location later.

You can use the bracelet to mark some box or location, so later you can find this location again. Couldn't find any other use for it.

I have read rumors saying it might be sidequest bound, but they got instantly debunked by others. In this reddit thread someone mentions to keep them as he says the following:

Collect them and something cool will happen

Finally, an article on Kotaku quoted the 1.04 patch notes, confirming what most people already suspected:

“Tracking bracelets are now sent to Recycler with ‘Transfer all Junk.’” In other words, you never needed to carry a discarded tracking bracelet around in the first place. This changes everything.

Once you find the bracelet, its owner is marked as "found" on security terminals, which counts towards your statistics and related achievement. That's all I've found during two playthroughts, and I doubt there are any other uses.

Interesting thing is that those persons bracelet belongs to are usually not found in game by normal means, e.g. you encounter Danielle only indirectly, seeing her through window of station.

There is only one practical use to holding the bracelets, and that's questionable at best. You're safe to recycle them.

Once you've found one, the owner is marked as "found" on the security terminals, as lentinant said.

The only (questionably) practical use for the bracelets is (fairly sizeable spoiler warning, from the last few hours of gameplay):

Shortly after Walther Dahl shows up, you get mobbed by Military Operators. You can disable your own tracking bracelet to stop him finding you, but he mentions that he's "closing in on" Alex. If you're carrying Alex's bracelet, the MilOps will continue to spawn in on you; by getting rid of it they will slow down from harassing you.