I'm in between. I agree using a tripod slows you down and that can make you consider the composition more thoroughly, as well as make your photography more disciplined in general. It's not just camera shake involved: for example, having the camera steady so you can systematically expose to the right may have a more dramatic impact on your eventual photo quality. But, other times moving around with the camera snapping things off from different angles is a more productive use of time, and I feel I'm learning more from having more shots to compare later, and more chance to experiment.
So, perhaps some combination of the two practices is best for improving your photography in general.
Quality wise, if you really think this shot is going to be your all time favourite, then by all means do everything to get it as sharp as you can. But if, realistically, you know it's just the best of what's around, and maybe won't even be the best for the day, that doesn't mean it's not worth taking but it might not be worth spending extra time on.
I'm generally happy with the images I get from my 5D sans tripod. Many of my lenses have IS too, so it's often practical. I do generally consider it a better use of my time, a better self-education even, to take more shots and not chase that last 1, 2 or 3 percent of quality. I could put that time in at work and move from 5D to 5DmkII and there'd be no question the quality would be more than 3% better. Or, I can use the 645E (always with tripod) and best a mkII. Not worth getting hung up on it. In 20 years time we'll have 200MP cameras and the IQ of these shots won't seem so brilliant anyway, but I want to be a better photographer then.