It is a bit difficult to tell what is going on from your screenshot, however, the basic answer to your question is yes - your low poly mesh needs to enclose your high poly mesh.
Your low poly mesh needs to follow all the major shapes and features of your high poly mesh. Think of it like wrapping your high poly mesh in wrapping paper. You can't have big spikes sticking out of your wrapping paper.
The purpose of baking a high poly mesh to a low poly mesh is:
- To get better topology (your low poly mesh can be created with good edge flow); and
- To bake all the very fine surface detail into a normal map so that its appearance is then created by normal mapping, and not actual geometry.
The trick is therefore to have your low poly mesh follow all the major shapes and features of the mesh, while ignoring the very fine detail (as this will be baked to a normal map). Sometimes that is a bit of a judgement call, but if you keep coming back to the wrapping paper analogy (what would you wrap around with wrapping paper, and what would you just paper over), it should be OK.