I would save my money here and just use a VPN. You are not that anonymous. Unless you are able to rotate IMEIs.
It depends on where you live and who you want to protect yourself against, if you live alone or have family members. In the thread about the Swedish police you can see how they tap the IMEIs and follow them live from cell mast triangulation and Bluetooth connections.
The police can for example just map the pattern of a family member living in same household as you, example wife using an iPhone.
They can request back logs from net providers where her phone has been triangulated, and after some months of data (even past data) they will see that for example when her iPhone travels, and when her iPhone travels there is another phone following her pattern very often.
They can assume that's you then. Specially if the date/ time or surveillance shows you were together too.
Checking the IMEI for that following phone will then reveal yours too and you are now being watched same as if you would have had a non anonymous card.
They do this often for people who use to have 2 phones, one for "work" and one for personal life. But can do this way to, to use someone related close to you to find you.