yes, A+ task points can grant you hearts.
Hearts are essential as they allow you to go further with girls.
For example if you have 1 heart, she might allow you to kiss her, but nothing more in that scene.
If you got 2 hearts, you will be able to touch her after kissing.
if you got 3 hearts, you will be able to undress her....
... and so on - i hope you get the gist. (these are just examples how the mechanics work)
There is no really a path on or off with any girl in this game, but scenes will end much earlier if you haven't enough hearts for that scene.
Aside that, no matter how many hearts you have, each scene will be avoidable by choice. /but maybe you'll miss another heart point.
So for example this update leaving Zoras home early to avoid her content