if an opponent moves unit off of battlefield before akali legend resolves, does the unit still go back to base?

No — if the unit is no longer in a showdown when Rogue Assassin's ability resolves, the ability's "move to base" instruction is ignored and the unit stays where the opponent's effect put it.

Rogue Assassin's [Action] ability reads "move a friendly unit in a showdown to base." That's the targeting requirement, checked again at resolution (Rule 359.3.e.2). If the opponent's reaction moved the unit off the battlefield (to base, another battlefield, or a non-board zone), the unit is no longer in a showdown, so it becomes an illegal target and the instruction can't be followed (Rule 359.3.e.5). The linked "ready it" (if Empowered) is ignored too (Rule 359.3.e.14.a).

Nuance: if the opponent's effect moved it to base, the unit does end up at base anyway — but that's the opponent's own effect doing that, not the legend. If they moved it elsewhere, it stays there. (Technically, if the unit was moved into another ongoing showdown, it would still satisfy "in a showdown" and the legend would still work — but that's not what's happening in the usual case.)