Of course it's possible. Etherium, for example, would make that sort of thing trivial.

BAT white paper and roadmap aim at full decentralization. Ethereum is not ready yet, either on scalability or anonymity via ZKP. We're working in phases using ZKP off chain accounting and single-monthly-transaction on, no fingerprint of users or their supported sites.

The token is an Ethereum token, so it's totally possible to do it in a decentralized way using a smart contract.

We're moving this into a whole new realm of problem then. Ethereum smart contracts have been shown as at the very least possible to get wrong by coding incorrectly, at this point multiple times.

I'm not sure taking a straightforward and easily reasoned about process that the courts could easily handle and moving it to something enforced by a programming language subject to bugs that are largely unable to be handled by courts is necessarily a step in the right direction. At least not until there's a lot more vetting of Ethereum and a much better and more secure ecosystem to call upon.