I don't see why not. There's another page about those screens here that states the backlight uses 75 mA @ 5V (it also says a boost converter is used, but that may only be for the next size up), and the 5V rail should be good for at least 1 A presuming the supply is sufficient.
That page also explicitly refers to the Pi Zero in the download link for OS images. Some of the Adafruit TFTs have support in the normal kernel, but apparently the smaller ones require something special, which is a bit of a downside, but at least the current custom image is fairly current. In case the point isn't clear, beware this means you need to use an Adafruit image, and not stock Raspbian.
The same links can be found via the product page here, and again the Zero is explicitly mentioned.
through the 40 GPIO pins, after they are soldered on them?
The header on the Zero is identical to the other 40 pin models (except without the pins).