Is there a correlation between how enthusiastic reviewers are and how much impact a paper has? If I have a paper which five reviewers agree is good, does that mean it'll probably also have high impact? Both reviewer enthusiasm and impact can be difficult to measure objectively, so I'm thinking of indicators such as the language used by the reviewers, the number of reviewers, whether the paper is accepted outright instead of revised, and the number of citations it generates.

From personal experience the answer seems to be "not really", but I don't have a lot of data, and I'm wondering if editors see a correlation or (even better) if there's been a study on this.
I doubt there could possibly be a measurable correlation. I don't know of anyone collecting data on "reviewer enthusiasm". But even informally, can you expect that in general enthusiastic reviewers is likely to result in more citations? 

Here I doubt it also, but only because the number of researchers in arcane subfields of a field isn't uniformly distributed. Your profile suggest that you work in Physics, which has a lot of quite different subfields. Some of those have a lot of current activity and others are more arcane. If you work in a popular field you are much more likely to get citations than if you don't. 

My own early work, for example, was rarely cited, but there were only about five people worldwide who worked in that tiny subfield. That was true even though the main result was very interesting. A lesser result in a more popular subfield would have likely generated more citations because more people could make use of it. 

However, there is enthusiasm and there is enthusiasm. If you prove a long studied conjecture that has been a bottleneck in your field, reviewers will be enthusiastic and the nature of the work will generate the citations. On the other hand, a great result the completes a field, meaning that there can be little follow up (rare, I know) would generate citations in the popular press, but, since there isn't any follow up, few in the scientific literature.