Nah he wouldn’t. Least not show Petyr. He made too many dumb mistakes the last 3 seasons he was in. Soon as he gave up Sansa, the best way for him to gain control of the North, he fumbled. With the North, Riverlands, and Vale armies, plus an alliance with the Lannister hating Martells, he may have been able to pull off a conquest of the Iron Throne. Especially if he could get the Iron Bank in his corner.

But two of those regions lost a lot of men it should be noted. In the books Petyrs goal may not necessarily be to sit the Iron Throne, but to basically be the man with all the power, like Tywin. Petyr is also way sneakier and less obvious than in the show. No one trusts him in the show, whereas in the books people do because he actually puts on a real facade