get "Velvia" like results in a jpeg strait out of the camera on a digital SLR. But I don't recommend trying.
It involves getting the "picture style", white balance, exposure, etc. exactly right at capture time. It could be done with a lot of trial & error if one were patient.
But IMHO the main creative advantage of digital photography is being able to post-process so that you can concentrate on getting a well-exposed sharp RAW image while you're shooting & deal with the details later, just as one needed learn to work in a chemical darkroom in order to really be able to get your images the way you want them. You'll need to bite the bullet & get Digital Asset Management software like Adobe Lightroom 4, Phase One Capture One, or several others out there (those are the most popular among professionals though). You can even shoot tethered from your computer & see what your camera's sensor is seeing (the 6D even does this over wifi, if you have plenty of batteries on hand :-).
A great website for learning digital photography techniques is Luminous Landscape. I suggest reading Michael's article on how digital camera exposure works
& what it means for your photos.
My experience with Lightroom (can't speak for C1) is that if you learn & understand the concepts that its tools manipulate, you can do far better than just "Velvia". It gives you the ability to really tailor the image to the subject matter in ways that could never have been done in a chemical darkroom.
If you're worried about the time that post-prod takes, make your most commonly used settings into presets & apply them in groups; you can really plow through piles of images in a hurry. Load 'em up, sort 'em out (& delete rejects to free up space), apply presets to the keepers in batches, look 'em over & tweak the best ones, publish to pretty much any web or print service you like (there are plenty of plugins out there), and yer done. Once you master digital asset management, you might look into getting yourself a pro-grade inkjet printer if you have more than an occasional need for prints (especially large ones).
Personally, having recently moved up from my trusty old 40D to a 6D, I can say that it's really pushed me to rediscover my love for photography, as *there just aren't any situations it can't handle* (within reason), and with the 40mm pancake it really becomes a "throw it in your bag & take it with you everywhere" camera.