Nope. The fission point is further back. Probably First Contact. Things were already different in Trek09 than they'd been in the original canon. Chekov's parents apparently met and had a baby a decade earlier, for instance. Shipbuilding is vastly different. NX-01
Enterprise -- which is part of this universe and doesn't fit the original canon (bad finale ignored) was approximately the tech level of the original NCC-1701 (and with one or two refits after the series was cancelled, is getting close to the same volume and engine output), while the NCC-1701 we see in Trek09 is roughly the size and tech level of the canon NCC-1701-D.
They've been trying to insist that Discovery and Picard are part of the original TOS-VOY canon, but they just don't fit, and I get mad at people who have worked on both who toe the party line. I heard KRAD talking at the Star Trek panel at ECCC last Spring and it made me furious.
He was one of the better authors of the ancillary fiction back in the late '90s/early '00s and knows the lore
amazingly well. To hear him saying, no, it's all the same timeline, and if you think it's an alternate universe you're just a hater... Ooo!

I know you like your paycheck, Kieth, but a little moral integrity would be nice.
So no.
If a Jen-Luc Picard is ever, in fact, born, as the timelines continue to diverge, it may not be in the same place or at the same time, and he may or may not choose to enter Starfleet, may or may not be in a position to take command of the
Stargazer, may or may not lose it to a Ferengi sneak attack, may or may not gain enough clout over the decade following his court-martial that he ends up with the Federation flagship, but that ship won't be the canon NCC-1701-D. There's a whole lot of "same-but-different" between the original and Enterprise timelines, but it definitely is
not a one-to-one mapping.