Can I play the effect of Gust Monk from my enemy trash?

Yes — "any trash" includes your opponent's trash, so you can banish a card from their trash to give a unit Assault 2 this turn (FAQ #11937).

One clarification on wording: that banish isn't "playing" the card — it's just removed from their trash and set aside, and nothing on it resolves. You still pick a unit to receive Assault 2, and the buff is dependent on the banish actually happening, so if both trashes were empty the trigger would be removed from the chain and do nothing. Also note that nothing lets you play Gust Monk itself out of a trash; you play it from hand as normal (paying the optional [1] extra for the trigger).