For grafting to "take", the the two plants' vasculatures have to be organized similarly. This is not possible for two such differently organized stems as a pepper and an apple.
This is a cross section of a young woody stem (such as an apple, though this example is a tilia):
This is a cross section of an herbaceous stem (such as a pepper):
You can see there is dissimilarity in organization. Furthermore, herbaceous plant stems die back in the winter.
Even if possible, grafting an herbaceous (non-woody) stem onto a woody stem (e.g. apple) would not confer any advantage for the green pepper, a tender annual, and would be disadvantageous to the woody stemmed tree (pruning for no reason, when the branch would otherwise have produced apples, and the leaves performed their useful functions.