If you fire a gun vertically from the earth's surface, but there is no friction, would it return to earth?

Yes it would return to Earth. The escape velocity for Earth is more than 11 km per second or 33 times the speed of sound. This is about 9 or 10 times faster than a rifle bullet.
So even without air friction the bullet’s going to go up, gradually slow down, and fall.
The problem is that without friction it’s going to come down too fast and kill someone at roughly the same speed as when it left the gun barrel.
In reality if you shoot a bullet into the air, when it drops it meets air resistance and winds up stabilizing at about 30–40 miles per hour. That’s enough to hurt you, but not as fast as if there was no friction.