On a 5DIII, no. Works fine on my 5DII, though, and I see no reason it wouldn't on the 5DIII. The aperture is not reported correctly (the TS-E lacks the necessary pins), but optically it's fine. The 2x works as well, although there's a bit of an IQ impact there.
You can view test chart images here using 1.4 & 2X, both MK II and MK III TC's: It looks like the MK II gets pretty fuzzy at 2X while the Mark III TC is noticibly better. The 1.4X MK II is not bad, but the MK III is sharper.