mmmm
It would appear not really in your case - if you got your phone anonymously, the dots would be connected via your carrier rather quickly.
You would need to take many more additional, rather difficult steps to prevent that from happening.
I also foresee a comment coming your way (which I know you know) about the fact that nothing guarantees perfect privacy. MAGFA will not stop trying to follow you around, you just decrease the instances/seseverity. Fingerprinting, among other things is quite an insidious beast... Still, totally worthwhile and feels quite good to make an effort to stand up for yourself. It feels, perhaps, a bit like a kindergarten: "it's my toy, you go and play with yours!"