Chile collects your IMEI to get a sim card.

AT&T does too for prepaid cards. If you pull the card out of an iphone to try it in an Android or vice versa it blocks the card.

They also will know your IMEI the moment you connect to the cell network.

But they might not know who it belongs to.

Only if you somehow acquired a SIM card which doesn't 'belong' to anyone.

It’s pretty easy to do in a lot of countries. The US doesn't require ID to buy some pay-as-you-go SIMs.

Of course, you could probably determine identity either from video cameras or, more likely, people using the phone and connecting to various towers, but you if you were diligent you could make it really hard.

I'm pretty sure the USA also collects all IMEIs...