Is AVM/TEAL compatible with verification of ZK-SNARK proof?

The answer is no. But work is being done here AVM: EC math by jannotti · Pull Request #4924 · algorand/go-algorand · GitHub that will add the ability to perform pairing checks, which are necessary to verify groth16 type ZK-SNARKs. The type used in e.g. Tornado Cash:

• Circuits
• Core Deposit Circuit