Does sleep deprivation cause sleep walking?

Possibly: Look at my health guide under sleep walking. There are several questions and answers about sleep walking. To answer your question directly, sleep deprivation can cause several things, notably psychosis, severe confusion and obviously utter exhaustion. There is where your question enters. If totally exhausted and you go to sleep there is a chance you could do some sleep walking. Not common but can.

Yes: People prone to sleep walking are more likely to do so when they are recovering (ie getting good sleep) after sleep deprivation.

Somnambulism: Sleep deprivation can contribute to sleep walking. https://www.sleepfoundation.org/articles/sleepwalking#:~:text=As%20sleep%20deprivation%20often%20contributes,bedtime%20to%20cope%20with%20sleepwalking.