Of course not.
But, as Margaret Wente points out (the first mainstream opiner to do so, as far as I can tell), it is a simulacrum of a genuine dystopia:
The anti-Christian narrative, that is. And in deciding to make fundamentalist, Old Testament-y Christianity the villain of her dystopia, novelist Margaret Atwood was every bit as "brave" as the boys who made Mormonism the target of derision in their silly creation (the one that, for obvious reasons, is not called/about The Book of Koran).The dystopia depicted in The Handmaid’s Tale really does exist, of course. But no one ever mentions it. It’s called Saudi Arabia, which is pretty much a dead ringer for Gilead. And, just as in the book, there really are parts of the world where homosexuals are strung up by the roadside. Iran and Chechnya, for starters. But you won’t read those things in the reviews because they don’t fit the narrative...
As for the prospect of Atwood's "prescient" horrors actually coming to pass in the U.S. of A., Wente notes that they've already arrived:
Two weeks ago, a medical doctor in Michigan was criminally charged for allegedly conspiring to perform mutilating surgical procedures on two seven-year-old girls, who were taken there in secret by their parents. These procedures are done in the name of religion. Where was the outcry, enraged editorials, and the protest marches from American feminists? The girls belonged to a Muslim sect who believe in female genital mutilation. So nobody paid much attention. In an effort to avoid appearing culturally insensitive, The New York Times even used the delicate phrase “genital cutting” in its reporting.