Yes, Tyson Bagent is expected to start in Week 3 for the Bears.
Caleb Williams suffered a hamstring strain in Week 2 against Minnesota. Ian Rapoport reported optimism it's a Grade 1 (mild) strain with a 2–4 week recovery timeline, so Week 3 falls squarely in that window. The Bears' official plan as of Sept 20 was that Bagent becomes the short-term starter while Williams rehabs (from the Tyson Bagent page).
If you're looking at fantasy implications — Bagent is a game-manager type who'll lean on the run game and short passes. Not a recommended streaming option in most formats unless you're in a 2QB/SF league and desperate.