I do all the time. But I read through the instructions carefully to make sure it was not prohibited. One company will not allow me to buy gift cards or alcohol. Another company just prohibits gift cards. I have not seen a single grocery that prohibits coupons.
I only do two grocery shops and both allow coupons, but they point out to make sure that the minimum purchase price is met AFTER you subtract the coupons.
Any grocery shop I've ever done has allowed coupons and store rewards cards. Be sure to keep the out-of-pocket amount at least equal to the reimbursement amount to get full advantage.