You could, but I believe you would find that Nix becomes pretty inefficient in that scenario. There is a surprising amount of overhead involved in setup/teardown of network namespaces and the other various sandbox features, and that cost is incurred for each individual derivation. It's a reasonable tradeoff for Nix when used as a package-level build sandbox, but (assuming my understanding is correct and still current) for Nix to work well as a file-level incremental build system it would require some strategic changes.
Here's the github issue with a bunch of related discussion and details: https://github.com/NixOS/nix/issues/179