Would masturbation be an effective natural way to induce sleep?

Could help. Masturbation can help relax you and it even tires some people out. Sometimes there is a sense of relief in reducing tension, in that way it can help with sleep.
Yes, it can be. Masturbation is a healthy exercise that can lead to relaxation and endorphin release, which can lead to overall relaxation, feeling of well being, and possibly ease you into sleep easier. With continued issues sleeping, consider alternative therapies as well, including sleep hygiene issues, such as making sure you sleep in a dark quiet bedroom with not 'blue' light , avoiding caffeine or alcohol.