Yes and no. 

They can pass laws which forbid use of cryptocurrency but they can never take away your rights to use them because it's out of their reach. They can't tap into the blockchain and connenct you with your wallet. The time you would get into trouble would be if you tried to exchange cryptocurrency for government issued toilet paper *khm* which fiat currencies are.

That's when they could track you down and link your wallet to your identity. But then again, there would be many different ways to circumvent this kind of oppression like buying technology goods like pc, tv, camera or anything of that sort with cryptocurrency and then sell it for fiat.

Conclusion

They can try but, they will never be successfull because people will always find a way to go around the obstacles they place in front of them.