Can you play Tideturner hidden in base?

No, you cannot play Tideturner hidden in the base.

According to Rule 737.1.b, the Hidden keyword allows you to hide a card facedown specifically at a battlefield you control. It does not allow you to hide cards in the base.

Furthermore, as clarified in the official FAQ:

• Ruling: Tideturner can only be played at the battlefield where it was hidden, not into the base to switch with units on other battlefields.