This sports shooter loves IS on long lenses and has been shooting with it for over ten years. I can take it or leave it on shorter lenses. But on 100mm and up, I prefer to have it.
Is does take a moment to get up to speed.... I'd say it's more like a half second usually, and really it's happening at the same time the camera is acquiring focus, so there's no loss. You're likely to have problems with both focus and IS if you really stab a shot, going from finger off the shutter release to full release quickly (but that would be lousy technique even if shooting film cameras and manual focus lenses).
Normally I've got the shutter release half pressed before I've even got the camera all the way up to my eye, so IS is already started. Then, using Back Button Focusing, I get the subject in focus. By then, IS is fully up to speed.
I've taken extremely fast shots "from the hip" that way and not had any trouble with IS lag... You can see it working and snap into a stabilized image in the viewfinder. Usually, if holding the camera reasonably steady, it's maybe a half second usually... not "a second or two".