Newb Q: T3i as Video Camera Replacement
Yes, you would need to continually focus as you shoot. And this is very difficult to do, because what looks great on the tiny screen can be really, really, out of focus when you view it on computer or TV.
The Nikons (D3100 and maybe the D7000, I don't remember) do continuous autofocus, but they use a technique that isn't very fast. Thus you might still have blurred pics.
If you want home videos get a video camera. You can find decent video cameras for hardly any money these days.
If you want the best of both worlds, then buy the video camera and look at refurbished T2is cameras from Canon Direct. If you happen to have a broken Canon point and shoot or other camera, you can get 20% off the price listed at the web site.