09-26-2013 03:14 PM
At the 100mm end of the zoom range, the lens becomes an f/6.3 -- and probably your camera can focus at f/6.3 ... but that's pretty much the limit. At the 400mm end of the range (and in fact even at mid-zoom levels) the 7D wont be able to auto-focus. The 5D III and 1D X have working phase-detect AF at f/8, but not the 7D. Pretty much all bodies hit the limit at f/5.6 (but usually you can sneak in f/6.3), but only those two bodies have working auto-focus at f/8.
If there is enough light, it may be able to focus in live-view mode becasue that uses constrast-detection AF, rather than the phase-detect AF points and if there's enough light and contrast it may be able to work, but contrast-detection isn't as fast so if this is for sports or action photography then that's probably not worth persuing.
You could always rent a 1.4x from one of the many rental agencies and give it a try to see if it works for you.