What if Nidalee dies but another friendly unit remains, do I still get to draw if I win combat?

No. Nidalee's ability says "When I win a combat" and defines winning as "I remain after combat." She has to be the one who survives — another friendly unit sticking around doesn't satisfy her trigger.

The combat result (Rule 466.3) is determined per player, but Nidalee's card text narrows her trigger to herself: if she dies from combat damage or any effect, she didn't remain, so she didn't win, and no draw occurs. Your team may still win the combat and conquer the battlefield with your surviving unit — that just doesn't trigger Nidalee.