Does teaching Chop the various tricks from the iFruit app actually serve a purpose in GTA V? Is anything useful gained in-game for Chop as a result of taking care of him via the app?
Chop is mainly just a distraction from the actual game and a way to show the player that the characters are humans and that they do normal things like walking a dog. One could completely neglect Chop throughout the game and nothing bad will happen. With that said, nothing good will happen to you if you're nice to him throughout the game. It's just a minigame that has no effect on anything.
One of the only useful things that Chop can do is quickly assassinate people while you walk him. This works best if you made him happy through the app as it will allow you to walk Chop and he will follow your commands.
Chop can also search for armor, health packs, weapons or scraps if you are near it, which makes it a very inefficient way to find things if you have no idea where they are, especially since you can find all of these items without Chop's help (there are maps available online highlighting the areas where the items are).