You can, but I found it messy and stinky. I use drums and a motor base. You can work in room light, you use less chemistry, and you're not inhaling chemicals from an open tray. It's a bit more up front investment, but it works great for me and others.
As has been said, you have less control over the process, which makes it both easier and potentially more frustrating. Primarily what's being referred to is contrast control. It's not like black and white where you have graded or multigraded paper. There are some tricks to controlling contrast in the color darkroom ranging from simple things like chemical additives to more advanced things like masking. You'll be happier, at least initially, working with negatives that are properly exposed and have a good range of tones.