Are bad orthotics worse for your health than no orthotics at all?

Can be: Orhotics are typically for comfort. If they don't feel better than not having them in, don't wear them.

Probably: Orthotics that are made with fairly hard material are very "controlling". If they tip your feet in the wrong direction, usually rolling inward, it can cause a lot of ankle, knee and foot pain. Soft, over the counter types of orthotics are of no help in my opinion. See a podiatrist for a good evaluation with some old shoes and your orthotics.

Definitely: A poorly designed device can lead to pathologic motion which in turn can lead to injury.