Doubtful. It's possible that Ten Rings were part of Hydra, as evidenced by a guy in Ant-Man was a member of both. Obadiah screwed over Ten Rings pretty badly. Treated them as hired guns.

Was Obadiah Stane apart of Hydra?

Obadiah first came to Stark Industries as a HYDRA plant to take control of the company. He quickly rises to second in command behind Howard Stark.

Who was Obadiah Stane to Tony Stark?

You might remember that the MCU's first villain was Jeff Bridges' Obadiah Stane, who antagonized Robert Downey Jr.'s Tony Stark in the business world and battled against Iron Man as the Iron Monger in super-suited combat. Stane ended up as a one-movie villain, but it wasn't originally intended that way.