In photographic terms an f2.8 lens is considered 'fast' and a f4 lens 'medium' whereas an f5.6 lens is considered 'slow' (this is of course to do with the amount of light it gathers). So if f5.6 is considered slow than f6.3 must be mega slow as it were. This is not always an indication of the focusing speed of a lens as the 400/5.6 proves but it certainly givers an indication where teles are concerned.
I assumed you were referring to the AF speed.
F6.3 is indeed slower than the very expensive primes or the 200-400 but Sigma has been releasing 6.3 telephotos for ages and they seem to AF just fine on Canon crop bodies (for the price, not comparing to the 600mm f4). Do not see why the Tamron could not.