Vive la différence would certainly be understood but being seldom used it looks to me more an “English” idiom than a French one, i.e. more likely to appear in a English text or conversation than their French counterpart and clearly after 1940 according to Google ngrams:

Note that while in English this sentence is often associated with men/women differences, this won’t be obvious for French people who would more likely associate it with cultural differences.

As a french person, I can presume that you’re right… Only english people use it xD
I’ve never used or heard that expression ! It can come out in a conversation, but… well… It will come like a “just-invented-expression” but that’s not a typical sentence… the same as if you say “Vive les carottes” 🙂

You ask about the phrase as it might/might not be used and interpreted by Anglophones and within France, so perhaps discussion of its importance in other parts of Francophonia is slightly off-topic; but

“[Haiti,] Vive la différence” has long been Haiti’s official {tourism} slogan.
(from ‘Caribbean Ports of Call’ via Google Books)
(See also paragraph 3 under “Early Boom” in this Wikipedia article on ‘Tourism in Haiti’)

The mid-1960s thru early 1970s bump in the phrase’s use as shown on this French ngram might indicate when Haiti began using it as its tourism slogan.
Regardless, that bump does correspond with the publication Cimarrón’s claim in 1988 that “… Haitian tourism officials have banked on for more than“…
… “twenty years … the slogan ‘Vive la difference!’.”

If Haiti’s use/adoption of the phrase as its official tourism slogan predates the mid-1960s, the five 5/6-year bumps shown on the linked ngram (starting in 1895 through 1958) could possibly be tied to the ups and downs of the Haitian tourist industry as described in the above-mentioned Wikipedia article.
However, tying Haiti’s slogan to the three large bumps shown in the 19th century and the coining/origins of the phrase would be far-fetched, imo (although Haiti did gain its independence earlier in that century).

Regardless, although perhaps not responsible for coining the phrase, the adoption of it (with the French spelling of ‘différence’) by Haiti, an independent (since 1804) Francophone member of the United Nations, as its official tourism slogan lends much more credence to it as an idiomatic French phrase that is worthy of recognition and familiarity, at least in my opinion, than a company choosing to use a phrase (‘La B/belle France,’ for example) as its corporate name or a political writer using it [sarcastically or otherwise] in a pamphlet.

Finally, although the differences between the lovely women of Haiti and its men are just as worthy of celebration as elsewhere on the globe, I don’t believe the notion of “differences between the sexes [as perceived by Anglophones or otherwise]” was behind Haiti’s decision to adopt the phrase as its official tourism slogan: it’s inviting us instead, in my opinion, to literally
“Celebrate Haiti’s differences [and diversity].”

“In April 1944 a proposal to ensure women’s suffrage and equality was presented to the French parliament. The presenter gave a lengthy speech, trying to emphasize the idea that women and men are actually the same. There is only one small difference. He never finished the thought, because everyone in parliament started to shout: “Long live that difference!” (Vive la différence!)”

-Velmir Srica (2014)