No. He's never going to drop her. Not within a reasonable set of circumstances, anyway. If the ship suddenly slammed into something and went tilting off course ... well, that shouldn't be counted against him.

He's gonna be extra careful about setting her down onto her feet in the wet shower stall, though. It would be very easy to lose footing here. Although the walls are so close together, it's doubtful she'd stumble enough to really hit the ground. At any rate, he's careful with her. She's also got a sturdy Han Solo to lean up against if she feels like she's slipping.

He's always happy to act in support of her.