Does an animation continuously set it's frame values?

I have a bool set to true on frame 10 and then on frame 15 it’s set to false. In between frame 10 and 11, if I have a script set the bool to false, will it automatically set it to true on frame 11?

Yes, each frame is copied from previous on each parameter.
Say, if you set a bool to true on frame 5, and then script it to false at frame 100 outside animation, it becomes true again on 101.
Great way to bypass it is to create 2 bools for the same parameter. Animation sets a bool to false, and the script sets another bool to true if current one becomes false. And doesn’t matter if the first one becomes true again.