If I soul harvest an enemy unit in a battlefield in which I have no units on, can my opponent play an ambush card to put that unit into the battlefield?

Yes — your opponent can play an Ambush unit to that battlefield in reaction to Soul Harvest.

Soul Harvest on the chain creates a Closed State, and since your opponent still controls the targeted unit at that battlefield, Ambush's condition is met: they may play a unit there and gain [Reaction] timing for that play (Rule 822.1.b). The Ambush unit finalizes and enters play immediately — you get no window to react to the unit play itself (FAQ #9326) — and then Soul Harvest resolves and kills the targeted unit. The Ambush unit stays, so your opponent keeps presence at that battlefield.

The only catch: they have to play it while the unit is still there. If they wait until after Soul Harvest resolves and the unit is dead, there are no units at the location and Ambush's permission no longer applies (Rule 822.3).