It really depends on how you count the Switch and Switch successor. But... no.
I'd say it makes most sense to simply count switch sales from PS5 launch on. I'm assuming the Switch will hover around 17 million, give or take 3 million for the next three years, and there's little chance of the PS5 selling that much.
PS5 definitely has better buzz than XBox atm, but it's not like the one where Microsoft was just constantly shooting themselves in the foot. Microsoft also won't be launching at 100 dollars more most likely. So, I think they'll do a lot better.
Unless you want to argue that Nintendo shouldn't count at all, I can't see PS5 having greater than 50% marketshare.