Is it okay to leave sciatia nerve pain untreated?

Depends: Treatment of symptoms like sciatica are a lot of time simply for better quality of life. Hence treatment is optional. However, if symptoms are persisting, it tends to be a good idea to at least see a doctor to confirm the diagnosis, and ensure there is nothing sinister causing the symptoms -- like tumor etc. But if you are having neurologic deficit, or bowel/bladder function change, seek treatment.

Usually Improves: Typically it improves within 3-6 weeks on its own as your body heals. If it continues then many different things can happen, chronic pain/numbness, muscle wasting from disuse or atrophy from significant nerve compression. In more severe cases, things like bowel/bladder incontinence or even paralysis can ensue. Would suggest seeing your doctor if you are not improving after 3-4 weeks.