I play a unit on my occupied battlefield, can an opponent play a reaction such as Gust?

No, you cannot react to a unit being played.

According to RiftJudge FAQ #1472 and FAQ #7795, units (and other permanents) leave the chain immediately upon being played without providing a priority window for opponents to respond. Because there is no priority window, you cannot cast a reaction spell like Gust to prevent the unit from entering the battlefield or to remove it before it arrives.

Key points regarding this interaction:

• No Response Window: Playing a unit does not grant priority to other players.
• Triggered Abilities: If the unit you played has a "When you play me..." triggered ability, that ability does go on the chain after the unit enters play. You (or your opponent) can react to that triggered ability, but the unit itself is already on the battlefield by that time.
• Removal: You can only remove a unit after it has successfully entered the battlefield and any "When you play" triggers have been placed on the chain.