Yes, you can certainly choose to not bill your insurance.
-at one time, my insurer only covered 20 of a particular medication I was taking per month. I could choose to get 20 covered with my regular $10 co pay and then the next 10 pills I paid full price for, or I could choose to take a partial fill. What I ACTUALLY did was ask them to send the script to a different pharmacy which I knew charged much less per pill for the medication but did not accept my insurance. It was almost $5 cheaper to bypass my insurance company altogether.
-I get 24 chiropractor/physical therapy visits covered (with small copay) per year. After that, I have to pay full price. If I leave the insurance company out of it altogether for those "extra" visits, I can pay the practice's cash-pay price and get a 20% discount off of full price.
As pp have said, if you're trying to fudge the system with controlled substances, I encourage you to stop, look at your life choices, and don't. In a legal manner, you don't want that juju in your life. In an addictions/abuse manner, you also don't want that juju in your life.