Technically, yes. Realistically, no.
If you find a really good deal on a replacement LCD PCB, the swap would be easy, but you'll almost never see them for sale and replacing the LCD alone is very difficult (and you're even less likely to find the replacement part).
That said, game Boys are dirt cheap on the used market, so it'll be cheaper and easier to just buy a new one and, if you're really attached to the housing of the one you've got, swap the LCD PCB in.