Yes, that lens is fully compatible with your Rebel. It exceeds the capability of your camera. Depending on what current lens you have the image quality will be equal or better. Whether or not you get great photos depends on you.
The EF 70-200mm f/2.8 lenses are pretty heavy and beefy lenses for Rebel body, most of which are not reinforced with some type of alloy chassis. Always keep the lens supported, and never allow the full weight of it to hang from from the camera mount.
As others have pointed out, the lens should work very well with your T7i. The image quality should be a significant improvement over any kit lenses that came with the camera.
"Always keep the lens supported, and never allow the full weight of it to hang from from the camera mount."
This is extremely important. It is a good idea on any camera but especially so on a Rebel.
"... will the pics be great even though it is not a full frame camera?"
Such a disappointing subject. Just keep in mind your Rebel is as full frame as any camera on the market. The fact is you get exactly what you see in the viewfinder. Full frame. Just like any camera model out there! Enjoy your new lens. It is the best zoom lens ever made perhaps one of the best lenses ever made, zoom or prime.