COCA has 28 citations for not my cup of tea since 1990 including uses in television and print news, various popular magazines, and in fiction. This suggests, as Mallory Elk notes, that the negation, at least, would be understood, if not especially popular. Indeed, it is more prevalent in Google Books' American corpus than in its British:
Compare this with the NGram for my cup of tea, which will include many references to literal cups of tea as well as the older senses of something well-accepted:
The 1984 edition of A Dictionary of Slang and Unconventional English, edited by Eric Partridge, notes
Since ca. 1940 perhaps just as often, if not more commonly, in the negative, as a polite rejection of someone else's proposal, demand, plea for help, etc. as 'I'm afraid that's not really my cup of tea', or 'Not quite everybody's cup of tea, do you think?'
According to the 1909 Passing English of the Victorian Era: a Dictionary of Heterodox English, Slang and Phrase, by James Redding Ware, cup of tea entered use around 1870 for a
Consolation probably suggested by a cup of tea being 'so very refreshing' to persons who do not drink any shape of alcohol. Used satirically of a troublesome
'Oh, don't yer though. You are a nice strong cup o' tea.' Cutting.
The OED attests to the use of cup of tea in print to refer to a particular taste or interest from 1932, in Nancy Freeman-Mitford's novel Christmas Pudding, and perhaps through popular literature such as this it crossed the pond. US servicemen stationed in Britain during the Second World War may also have brought it back; the entry for this expression at (UK-based) The Phrase Finder notes
This negative usage began in WWII. An early example of it is found in Hal Boyle's Leaves From a War Correspondent's Notebook column, which described English life and manners for an American audience. The column provided the American counterpart to Alister Cooke's Letter from America and was syndicated in various US papers. In 1944, he wrote:
[In England] You don't say someone gives you a pain in the neck. You just remark "He's not my cup of tea."
The change from the earlier positive 'my cup of tea' phrase, to the dismissive 'not my cup of tea' doesn't reflect the national taste for the drink itself.