If I use tornado warrior to empower Tail-Cloaked Matriarch to summon a shen can his reaction make him be played to a battlefield with friendly units

No — Shen, Kinkou played by Tail-Cloaked Matriarch enters at your base; his Reaction can't redirect him to a battlefield.

The Matriarch's "When I become Empowered" trigger is a Limited Play Effect (Rule 419.3) that fixes the destination: "Play it to your base, ignoring its cost." Shen's [Reaction] only grants timing permission (Rule 813) — it lets him be played at Reaction speed and to a battlefield you control when you play him normally, but it can't override a location already dictated by an effect.

Note that Shen, Kinkou (3 Energy, 1 Power) does qualify for the Matriarch's trash search, so he can be summoned — he just lands at your Base. If you want Shen on a battlefield, you'd need to play him from hand as a Reaction at a proper window instead.