DinoCharacterFoodDrainMultiplier-parameter does influence the taming-speed, because the unconcious dinos also use this parameter (with another one) to calculate their food-drain. To compensate the longer taming time you could increase the
TamingSpeedMultiplier in a reciprocal way. That is not possible if you set the food-drain to zero, of course.
I don't know, how the taming-experience will change. It could be with extremely changed values that a dino will not eat for a long time, then eat one piece and get tamed. Making the taming time similar, but the taming experience will be different.
Also see this post on the steam-forums for the same question: https://steamcommunity.com/app/346110/discussions/0/530647080129304242/
To solve your original problem: How about just shut down the server for some time? Or save the world and if you reconnect after a long time load that savefile again. That would solve the issue without having to manipulate the settings.