I can't confirm but quit using the free day and $ off coupons for exactly this reason. One phone rep (Visa) told me a free day earned from the rental program voids the card's CDW but a free day coupon does not. Another phone rep told me any free day voids it. I could never get anything in writing either.

To a point I'm even a little concerned about the 10% discount you get with the generic Emerald Club Contract ID, but less so since it's not marked as a coupon on the contract in the same way.

At the end of the day the small savings wasn't worth the peace of mind.