Dwdallam,
In my experience the IS functionality on the 70-200L IS makes a considerable difference in compensating for the sort of vibrations that you describe.
My Canon 70-200 f/4L IS manual suggests turning off IS when using a tripod but enabling IS when using a monopod or a tripod with only two legs extended. This instructions appears to assume that a tripod-mounted configuration is perfectly stable, which of course is nonsense. I have also read forum suggestions that leaving IS on with a tripod-mounted shooting configuration can cause problems.
I do not believe that the gyro-based IS system in the lens "knows" whether camera shake is a result of your trembling hands or tripod vibrations. (I am not absolutely sure of this, because a different time constant may be associated with the two causes of camera shake.) In my experience, though, as I said, IS appears to be just as effective in both cases.
In fact, the 70-200 with x1.4 converter on my 40D (x1.6 factor), mounted on my Gitzo 2540, is so unstable while focusing using live view at x10 magnification that I can hardly focus the jumping image unless I press the shutter release half-way to engage IS. Then the image settles down to a remarkable degree. (Actually, the image settles "up.") If you are using a non-IS 70-200, I would trade it for an IS version as soon as possible. The difference in image stability for long-lens landscape work is well worth the price difference.
Another question is your method of shutter release. I no longer bother with the remote shutter release. I use the two-second timer instead, and find that the two seconds is more than enough time for the vibrations caused by manually pressing the shutter to dampen. (Obviously, manually pressing the shutter release without the timer will not fly at these focal lengths.)