Perhaps that's the particular formulation for some people, but that only makes sense in a post 2000s American evangelicalism. The principle of Christian nationalism is in the name, they want a nation for Christians by Christians. A theocracy in a sense.
However, having come from that background, I can confidently say that is not how your average evangelical formulates it in their head. What I'll grant is that they both have an eschatological makeup but that's a given with evangelicals—thats basically their thing behind a personalized designer jesus