Sure, lots of people do it; you may see results within a couple more weeks, or if your decrease in laying was caused by an oncoming molt rather than daylength per se you might not.
Please make sure it is secured by something other than just the spring-loaded clip, though. Although a regular lightbulb is less likely to start a fire than a high wattage heatlamp bulb, it can still happen if the light falls down, and you would be surprised at how many things can cause that. Secure it STRONGLY, and ideally make sure it is caged so a flying chicken can't break the bulb either.
My coop has solar lighting! I bought some of those solar yard lights, mounted the collectors on the roof of the coop, and put the lights inside. It probably isn't the greatest for egg production as the intensity of light fluctuates with the solar input.