Does diazepam make you sleepy

Yes, it does.

It is even sometimes prescribed for insomnia to take advantage of it's ability to make you drowsy - although insomnia has also been reported as a side-effect in some people taking it for other reasons.

Drowsiness, dizziness, blurred vision, or headaches are known possible side effects. If any of these effects persist or worsen, notify your doctor or pharmacist promptly.