In my estimation, that usage clearly calls for an em dash, not an en dash.
CMOS Online's FAQ re: hyphen, en dash, em dash says:
The en dash connects things that are related to each other by distance, as in the May–September issue of a magazine; it’s not a May-September issue, because June, July, and August are also ostensibly included in this range. (...)
The em dash has several uses. It allows, in a manner similar to parentheses, an additional thought to be added within a sentence by sort of breaking away from that sentence—as I’ve done here. Its use or misuse for this purpose is a matter of taste, and subject to the effect on the writer’s or reader’s “ear.”
(highlighting of the relevant em-dash guideline is mine.)
Similarly, PunctuationMatters.com says
- Joins numbers in a range, such as “1993–99” or “1200–1400 B.C.”
- Joins words that describe a range, like “July–October 2010”.
- Works better than commas to set apart a unique idea from the main clause of a sentence
- Separates an inserted thought or clause from the main clause
The Grammarist also has something to say on the matter:
Em dashes can replace colons or serve as harder versions of commas (similar to semicolons). While parenthetical em dashes often operate in pairs , hard-comma em dashes often function alone at ends of sentences, for example:
The all-renewable energy sector is 30 years away—and always will be. [Salon]
Your example sentence is identical in structure to the Grammarist's example, and is consistent with the other sites' guidelines for em-dash usage, but not with the guidelines for an em-dash. Thus I say that an em-dash is correct there, and using an en-dash instead would be a mistake.