This is an interesting concept.

You might look at Ethereum, it is a blockchain driven contract engine with a turing-complete language for scripting. You can do anything you can mathematically define. This contracting language goes far beyond Bitcoin's abilities.

Since a computer virus isn't much different being code at the core, you could very likely build a self-replicating contract that can auto-execute other functions. Ethereum contracts are essentially autonomous agents that can perform many functions.

Part of the Ethereum project is to have compilers that you could translate viruses written in another language into Etherum LLL.

ethereum.org