Can you empower something that does not have empower?

Yes, you can. The Empowered status isn't locked to cards that have the Empower keyword.

Empower is the keyword (an activated ability you pay for), but empower is also a game action (Patch Notes 2026-07-17). Cards like Sanction ("Empower a unit"), Mournful Witness ("when a combat that I was in ends, empower me"), and Hextech Formula ("[T]: Empower another gear") can grant the Empowered status to any unit or gear, regardless of whether it has the Empower keyword printed on it.

The Empowered status does nothing on its own (Rule 827), but if the card has an [Empowered][>] ability or another effect that checks for it, the status will turn those effects on.