Is the 17-70 good enough for indoor non-flash photography, as I don't like using a flash where possible?
I wouldn't rely on it for that. Much depends on what your subject is and whether or not there's movement. If there's possible movement, then you may need something 'faster' than 2.8. If there's no movement then it's a matter of keeping the camera still for the longer shutter speed you'll need (i.e. it may require 1/15 to capture the shot) - which is why so many people like IS lenses.
But, people who do a lot of indoor no-flash work will typically work with faster prime lenses.