That very much depends on what you choose to regard as the 'true nature' of the AI. In other words we're flirting with reification fallacy by regarding the AI as a whole as 'living on the blockchain', or even being 'driven' by the blockchain. It's important to fix in mind what makes the blockchain important to such an AI and to its autonomy. This, I believe, is always the financial aspect. The on-blockchain process is autonomous precisely because it can directly control resources; it loses autonomy in so far as its control of resources no longer fulfils its goals. If you wish, you can consider the part of the AI which verifies correct computation and interfaces with 'financial reality' as being its real locus of selfhood, but bear in mind that even the goal description/fulfilment logic can be zero-knowledge proofed and so exist off-chain. From my perspective, the on-chain component of such an AI looks a lot more like a combination of robotic arm and error-checking module.
The cryptocurrency ethereum is mentioned here occasionally, and I'm not surprised to see an overlap in interests from that sphere. Vitalik Buterin has recently published a blog post discussing some ideas regarding how smart contracts can be used to enforce superrationality in the real world, and which cases those actually are.