Starving has no influence on taming effectiveness. In fact, it can make it worse if you let them starve until it harms them.
There are only three things that influence taming: how much health the creature has when it's taming, how many things it has eaten during taming, and how many of the same creature you've tamed before.
The more health the creature has when being tamed and the more of the same creature you've tamed before, the higher the taming effectiveness. Being able to knock something out with minimal damage to its health is very useful, because it has a really big impact on taming effectiveness. Taming creatures isn't a bad way to build taming effectiveness, either, if you're patient, but some of the bigger creatures might be a pain in the ass to tame and tame and tame again, and you might not have the food income to take care of them all, anyway.
Inversely, the less things the creature has eaten while being tamed, the higher the taming effectiveness. Narcoberries and narcotics don't technically count since they don't directly impact taming effectiveness, but feeding narcoberries to a carnivore or narcotics to a herbivore mid-taming does decrease the level the taming is at. If you're short on one, you can starve a creature while feeding them the other so that the actual taming part goes quickly and you don't need to use as much of the stuff you're limited on, but once you're in the middle of taming, you want to use the preferred drug exclusively.
Finishing with a higher taming effectiveness supposedly increases the tamed attributes, and it seems like it's true from what I've seen, but I'm not positive about it, because I've seen a bit of disproof, too. Either way, the taming effectiveness can have a big impact on just how long it takes to tame a creature.