I use the same Kenko 1.4x for Canon and there's very little image degradation TBH. There is some, specially if you get the exposure a bit out, but not enough to make me not want to use it.
I don't know much about Nikon lenses but with the Pro300 it even retained AF with a Canon 7D and 5D2 with a Canon 100-400 f4.5-5.6 L even though it reported the lens as f8, which on a Canon only the 1D series should AF at f8, while the rest should stop at f5.6.
Bearing that in mind you may retain AF on the Nikkor AF-S 70-300mm 4.5-5.6 IF lens you have.