Will I be able to get a drink at a restaurant without an ID?

Whether you are "carded" depends a lot on how old you appear to be and to act, plus whether you are with young people or older adults, plus the type of establishment (restaurant, bar, combo, etc.) Just order what you want, calmly and directly. If you are "carded", say you are sorry but don't have your license with you, and order a soft drink.