Could you add this basil sugar to the cake batter and have it bake inside as well as topping it?

I see no reason why not. It will make the cake green - or at least full of green speckles, but, hey, if it tastes really good, go for it. You don't want to increase the amount of sugar that much, however, as that could affect the structure of the crumb.

If you try this, let us know how it turns out, please! ;o)