Can I use my Akali legend to move a unit back that moved into an uncontested battlefield?

Yes — as long as it's your turn and the showdown at that battlefield has actually started.

A unit moving into an uncontested battlefield you don't control applies Contested and stages a Non-Combat Showdown. Once it begins, you're the player who applied Contested, so you have Focus, and Rogue Assassin's [Action] ability is legally timed during a showdown on your turn (Rule 347.1). Activating it moves that friendly unit back to base — and readies it if Akali is Empowered.

Caveat: if that was your only unit there, the showdown closes with no unit remaining — no Conquer, the battlefield becomes uncontrolled, and you can't play units to it afterward. Also, if the showdown hasn't opened yet (e.g., something's still on the chain from the move), the unit isn't "in a showdown" yet, so you can't target it.