[Now that is a lovely personal challenge! ...Cecil hopes their trainer is fine with it, though.]

Levels, preparations and the items at your disposal can influence the results, as I'm sure you know, but Dark-types are not particularly disadvantaged against any of Kanto's Gyms. If the Absol in question is strong enough and can endure the length of the matches, defeating them all single-handedly should be possible. The biggest potential problem would be Viridian.