Prey explains the two conditions under which Prey targets are chosen: “After deployment but before the first player’s turn” and “When the prey is destroyed or removed from play.”
There are no other limitations provided, beyond “choose an enemy model/unit.”
So, after deployment (which seems logical to interpret as Deployment, i.e. "When players place their models on the table at the start of a game, they deploy them to a deployment zone. "), the player with Prey chooses a prey target.
Given the rules quote for Line of Sight & Targeting, models do not have to have LOS to models to choose them. So, it seems logical that yes, the model with Prey can choose a model that has not been deployed. If this said “target”, this would be a very different situation.
I can’t find any rules around game effects or anything of that nature that require models to be in play to have game effects on them. All the situations I looked up either specify when effects can be applied or when they expire. There does not seem to be a blanket rule that would apply.
Note that, based on #1, if at the start of the game you choose another Ambushing model/unit as your prey, and your opponent never deploys the model that has been chosen as prey, you never have another opportunity to choose prey. So…be careful, I guess.