An "average" interior lighting level (EV 5 at ISO 100) would require 1/8 sec at f/2 at ISO 100, 1/30 sec at ISO 400, and 1/60 at ISO 800. Shooting 50mm on a crop camera, and using the "rule" that hand-held shutter speed should be no less than the reciprocal of the focal length, your minimum shutter speed would be probably 1/60 sec. That means that if you shoot your 50mm f/1.8 lens wide open, you'd need to bump the ISO to at least 800, to be able to shoot at 1/60 sec. At that aperture, if your subject was 10 ft. away, your depth-of-field would be a little under 0.8 ft. (about 10") "thick". So, you will get most of a person's head in focus, but not the person standing behind them or in front of them. If that's unacceptable, then you will need to increase the aperture to f/5.6 or even f/8, which means a loss of 3-4 stops of light. If you had a 5DIII, you could boost the ISO to 12,500 (4 stops from 800), and get decent images. Can't do that with a Rebel. So then flash becomes the way forward.
To recap: f/1.8 will allow you to shoot at 1/60 sec at ISO 800, with a rather thin Depth-of-field. If that's what you want, then yes, it will allow you to take the picture without flash. But you will have some noise in the images, and the depth-of-field will be shallow.
