Use Enzyme for Integration Testing (end-to-end testing)

Several people have reached out to me regarding integration testing with Enzyme. While Enzyme is currently intended only for "Unit" Testing, I think that there is significant value to be extracted from Enzyme's API that could be used in the context of an integration test.

I'm not sure what this looks like yet. We could integrate with another (mature) integration testing framework, or we could build one ourselves and include it in this project, or we could build another project that depends on enzyme, or {insert your idea here}.

I'm creating this issue as an initial discussion grounds for people that are interested in this, and would like to discuss or propose ideas.