Can Rengar Trophy Hunter use Ambush to play to base?

No, Rengar, Trophy Hunter cannot use Ambush to be played to your base.

According to the rules and FAQs regarding Ambush:

1. Ambush Restrictions: The Ambush keyword (Rule 822.1.b) specifically grants permission to play a unit to a battlefield where you control units.
2. Rengar's Unique Permission: Rengar, Trophy Hunter's card text provides a specific, additional permission: "I can [Ambush] to a battlefield where there are enemy units, even if you don't have units there."
3. Base is not a Battlefield: Neither the standard Ambush keyword nor Rengar's specific text grants permission to play him to a base using reaction timing. As clarified in RiftJudge FAQ #10089, Ambush only adds valid battlefield locations for reaction-speed play.

If you wish to play Rengar, Trophy Hunter to your base, you must do so during your Main Phase when the game state is Open, using standard [Action] timing.