Yes, DSLRs are a good starting point for doing movie type projects. The use of interchangeable lenses and the shallower depth of field offered by larger sensors than found in most consumer video cameras allows for far more artistic options. This is why DSLRs are very popular with the amateur film making community.
It should be noted, however, that they are not without their drawbacks. All but the most recent DSLRs (including the 600d) lack auto-focus while shooting video, so you will have to either focus before shots or manually adjust your focus during the shot. (If you move up to the 650d instead and use STM lenses, it IS able to auto focus when shooting video.) Focus peaking can help with this by providing highlighting of the most in-focus points in the image, but it requires the use of custom firmware software like Magic Lantern. (I've personally used ML, but it isn't without some small degree of risk to your camera.)
Additionally, DSLRs suffer from something known as a rolling shutter. On a high end video camera, the entire image for each frame is captured at the same time, thus quick pans look crisp. On a DSLR however, the sensor is scanned line by line when shooting video, so fast pans result in a "jello" effect (which is well documented with numerous videos demonstrating the problem on Youtube).
It is also worth noting that you do still get what you pay for in quality. A near bottom of the line consumer DSLR, particularly with a dirt cheap kit lens that comes with it is going to have much more marginal quality than anything professional. Even a higher end entry level model like a t4i (650d) or better yet, a mid-range model like a 70d will have far superior quality. Similarly, replacing the kit lens with something like a 50mm f/1.8 prime or other better quality lens will result in a substantial improvement in video quality.
It still won't be anything near Hollywood level though. About the closest you can get to Hollywood quality for under $7,000 is a 5D Mark iii running ML and shooting RAW footage on high end L optics, but even at $3,500 for the camera body and $1,500 to $2,500 for the lens, the quality still ends up being noticeably lower (to the professional eye) than a professional video camera like an ARRI Alexa (which costs $50,000+), but it is close enough to raise eyebrows in the professional community.
That all said though, DSLRs (even the basic models) still offer more bang for the buck in terms of artistic control than almost any consumer level camera, just so long as you also realize they are harder to use for video than a consumer camera, which can handle more for you, but gives you less options.