Yes, you are still charged. Free dining plan only allows for dining credits for free, it doesn't cover your tips, cancellation fees, or alcohol. When you book, you'll still be required to secure with a credit card.
Restaurants are only paid for the dining credit if you actually use them. If you don't show up then they aren't paid. This is whether you are taking advantage of a free dining promotion or paying for your dining plan. The restaurants are paid the same regardless and it isn't free to them. It's WDW Travel Company that is giving the credits to you for free with this promotion. Restaurants receive the same re-embursement for the credits regardless, but only if they're actually used.
Short answer is yes, no show fees are always in effect at the eligible restaurants regardless of dining plans, promotions or anything else.
There's a no-show charge at the restaurants listed in the sticky thread on this forum no matter what time of year it is or how one is paying, free dining or no free dining.
If, as Disney says, they instituted this policy in many restaurants to avoid having guests make multiple reservations for the same time and then just not show up for most of them, free dining would likely be prime time for that sort of thing to happen.