Can a woman who works out get six-pack abs by exercise alone without using illegal steroids?

Yes. Definitely "doable" the natural way. Also take a moment to consider your body image & what your goals are. It may be better to focus on general wellness than one particular anatomical feature. What good is a six-pack if you have to stress yourself out to get there?
Good abs &l ifestyle. Lean abs can be achieved naturally when women have low body fat about 20-25%, strong lean muscles as well as a diet that is low glycemic (so more plant based, lean proteins, water), avoid the refined and processed foods.