Well, I've never tried it, but I'd imagine that saucing every other round would be inconsistent as well, the rounds where you did sauce it would feel one way, the rounds where you didn't it would feel different.
This really only applies to carpet tracks that have a groove built up (tracks where the layout doesn't change often or that see a lot of use between layout changes) and get heavy groove built up. In many cases the tires come off the track feeling very sticky and gummy from picking up the buldup during the run. Cleaning between rounds or running a different set of tires each round are the only ways I know to maintain consistent handling throughout the race day.
Trips