Short answer is no, completely different set of connectors and fit. You can see on the Slim design that the LCD slots into the top with the bezel already fitted (less expensive to manufacture), whereas the OLED on the Phat is just the screen underneath the one-piece front cover.
As someone who owns both I can tell you the LCD screen on the Slim pales (literally; the colours are way less saturated) in comparison to the OLED on the Phat models. The build quality in general is better on the 1000 series Vitas, the Slim feels cheap and plasticy in the hand, the analog sticks don't feel as smooth, all sorts of little details. Only thing I would say is better is the smaller touchpad so it doesn't get unwanted inputs as much, a big thing if you're using it for PS Now/Remote Play which is the reason I bought mine.