Yes, of course it will. Generally speaking, if you do not sleep well and are lack of sleep, it will be easy for you to make your eye to twitch. There are a few causes that can cause your eye to twitch. It includes dry eyes, stress, caffeine, lack of sleep, or harsh light conditions. For example, for your situation, you did not have a good sleep, so it will make your eyes be stressed. In that way, it will be possible to make your eyes to twitch. So to solve this problem, you may just do some measures to make yourself to have a good rest.