To check out a used lens, take a small flashlight with you and inspect inside. There will likely be a few specks of dust, which will not be any problem. Just look for element separation, fungus, any flaws in the coatings, things like that. If you don't have a flashlight, you can hold it up to a bright light source and look through though a flashlight you can hold close to the lens tends to work better.
As mentioned, the main thing is you'll have to keep your shutter speeds up when shooting handheld. On your crop cameras you should probably go for 1/640 minimum, 1/1000 would be even better if you can mantain it. You may need to bump up your ISO to 1600 to get fast enough shutter speed. If/when you need to shoot slower shutter speeds, try a monopod and/or a tripod... and learn to do mirror loskup for really slow speeds. A long tele exaggerates even the slightest movement.
If forced to use a slower shutter speed and there's nothing at hand to help steady your shot, set your camera to its highest frame rate and take extra shots, plan that some of them will show some camera shake. It's also possible to make a "poor man's tripod" with a five or six foot long piece of 1/4" or 3/8" rope and a 1/4 x 20 bolt. Tie the bolt in one end of the rope, screw it into the tripod mount of the lens, let the rope drop to the ground, step on it with one foot so that the rope is nice and taut. You can usually get a couple stops slower shutter speed with the extra stability from that. Plus you can wad up the rope and stick it in a pocket.
With your camera, I think you'll be limited to the center AF point only with an f5.6 lens.
It's too bad the 400/5.6 doesn't have IS, but that would add another $400 to $600 to the price, plus a bit of size and weight I'm sure.
The image below was shot handheld on an moderately overcast day with my 300/4 IS with 1.4X (420/5.6 effectively) on a 7D, at f5.6, ISO 400, 1/400 shutter speed, but that lens has IS. I should have used a higher ISO to get a faster shutter, but was shooting fast and didn't really have time to change the ISO. It's a wee bit soft in larger sizes, but that might be due to the teleconverter as much as the 1/400 shutter speed...
Same lens and teleconverter, except on a 5D Mark II at ISO 1600, f8, 1/250 shutter speed... and I might have used a monopod:
Shouldn't be any problem lugging the lens around, it's not much bigger or heavier than your 70-200/2.8 with the 1.4X on it. IQ with the 400/5.6 alone will likely be better than your zoom + 1.4X or my 300/4 + 1.4X. You will probably find the built-in lens hood convenient, too.