No, Felix Yusupov was just a useless nerd who thought he knew how murder worked because he’d read a book.
Based on the available historical evidence, the most likely sequence of events is as follows:
The conspirators attempt to kill Rasputin with poison-laced cakes, but fail; it’s unknown whether this is because de Lazovert fucked up the poison, because Rasputin – who had a well-known dislike of sweets – didn’t go in on the cakes as heavily as they expected, or just because a poisoned cake is a really stupid idea.
Seeing that the poison has failed, Yusupov gets Rasputin alone for a moment and shoots him once in the chest, causing him to fall senseless to the floor. Because he’s a useless nerd who thinks he knows how murder works because he read a book, Yusupov is unaware that a single handgun shot is very unlikely to be immediately fatal, and neglects to finish Rasputin off, instead leaving the room to confer with his fellow conspirators.
When the conspirators return to retrieve Rasputin’s body, he recovers from the shock of the initial gunshot and attacks them. Following some general panic, a third conspirator, Vladimir Purishkevich, opens up guns blazing; Purishkevich manages to miss several times in spite of being at point-blank range, but eventually strikes Rasputin in the head, killing him instantly.
The conspirators beat the shit out of Rasputin’s body just to be sure, then proceed to make a complete clownshow out of disposing of the corpse; the remainder of Rasputin’s injuries are sustained postmortem.
Pretty much everything else about Rasputin’s miraculous invincibility is invented whole cloth, much of it by Yusupov himself in order to build himself up in his own published memoirs.
(As icing on the incompetently poisoned cake, elements of Yusupov’s memoirs were later incorporated into the 1932 film Rasputin and the Empress, which led to Yusupov suing MGM Studios for libel because the film strongly implies that Rasputin was fucking Yusupov’s wife. The precedent set by that lawsuit is the reason those “similarities to any real person living or dead are coincidental” disclaimers exist.)
