If Nidalee moves into a Galio and cannot kill it and gets pushed back to base, does Nidalee draw since she remained alive?

No, Nidalee, Cat Form will not draw a card in this scenario.

Explanation

According to Nidalee's card text, her ability triggers when she wins a combat. The text clarifies, "(I win if I remain after combat.)"

In your scenario, Nidalee is "pushed back to base" (recalled). Per the rules for combat showdowns, if a unit is recalled from the battlefield, it is no longer present at the battlefield for the final combat cleanup/resolution steps. Because Nidalee is not present at the battlefield when the combat result is determined, she does not "remain" at the battlefield after combat. Therefore, she does not meet the condition to win the combat, and her ability will not trigger.

Sequence of Events

1. Combat Damage Step: Combat damage is dealt. If Nidalee is not destroyed by Galio (or vice-versa), both units remain.
2. Recall Effect: Some effect pushes Nidalee back to her base (e.g., an effect like Symbol of the Solari, or a recall effect triggered by the combat state).
3. Determine Winner (Rule 461.3): The game checks the status of the battlefield. Since Nidalee has been recalled to her base, she is no longer at the battlefield.
4. Result: Because she is no longer present, she cannot be considered to have "remained" at the battlefield, failing the win condition for her ability. No draw occurs.

This is consistent with the established logic that a unit must be present at the location of the combat during the resolution step to be considered the winner.