Does sneaking increase catch success?

The useful part is that the bonus is earned before the catch attempt, not during it. Stay behind the creature while you close the distance and the backstep bonus is applied to the throw. Walk up to it from the front and you get the plain odds. So the approach is the skill here, not the timing of the catch itself.

It is a bonus, not a guarantee. A backstep approach raises your chance on a wild Aniimo, and it can still fail. Treat it as the cheapest thing you can do to improve a catch, since it costs nothing but patience.

Sneaking is also not the only lever on capture success. The Tumbler raises capture success in specific situations, and during gather events it reaches a 6x multiplier. That is a much bigger swing than an approach angle, so if you are hunting something you badly want, the event window matters more than the direction you walk in from.

Alpha Aniimo do not work this way

A wild Alpha is not catchable at all until you have beaten it in combat. There is no sneaking your way past that step. Once it has been defeated it becomes catchable, and the fight is what opens the window rather than the approach.

Not settled: How much the backstep bonus actually adds, and whether it stacks with the Tumbler's multiplier, is not settled.