Can a teammate invite another teammate to play ambush unit in a state?

No — the 2v2 invitation only lets you play spells and activate abilities on your teammate's turn, not play units, so an Ambush unit can't be played off an invitation in an open state (Rule 489.8.a; FAQ #3647 lists spells and abilities only, explicitly excluding units and gear).

Two related caveats worth knowing. Ambush's [Reaction] is a conditional card permission, so a unit with Ambush can be played in a Closed State on any player's turn if you have priority (Rule 813.1.c.1) — that's the card's own permission, not the teammate's invite, and it still requires you to already control units at the destination battlefield. And you can never play it to a battlefield controlled only by your teammate, since control isn't shared (Rule 489.8.c; FAQ #7273).

If the Ambush unit is being played to your own Base, the Reaction permission doesn't apply at all — it's [Action] timing only (FAQ #10089), so no invite-based play there either.