Not really. It leaves a trail. The only problems with tracing is jurisdictional. If they can tie you to a particular "wallet" on their currency and by law, it's over. You won't ve able to buy or sell without leaving a clear, easily searchable trail, unless you trade in kind.

If the ID is required for access to the internet, they'll know if you traded other crypto-currencies.

The libertarian game then shifts to stealing or spoofing identity. Gurps cyberpunk is the real future.