You technically can, and many people have done this and similar effects for "interest-gaining" rewards, where they would take out balance transfers and other intro APRs in very specific ways to deposit the free cash in the bank and earn some interest on it, all the while paying the minimum payments. Then, when the offer is set to expire, they return all the money and PIF the card. Only problem with doing what you propose is that you don't actually get rid of the debt, just move it around, so you may not qualify for another 0% APR balance transfer at the time if your utilization is still too high. Other things to watch out for are balance transfer fees, so even if there's no APR on the BT, you can still get hit with a $29 fee or 3%. Read the fine print.
Hope this helps!