I think a government with your goals would be way more effective if it just slapped a unique id on every dollar, and tracked all the transactions from the central ledger it already has.
Not possible with paper money. VERY possible with a blockchain.
Dollars are already tagged with unique serial numbers. Just track who took out the paper, and who redeemed it, in the exact same centralized ledger that tracks all the other dollars. Same as with Casascius bitcoins.
Besides, blockchain IS just an accounting ledger. The only difference between it and the central bank ledger is who decides the rules that it must follow.