Can we put Document Creator report layouts under source control?

Yes, you can. Starting from Document Creator 2.0.0.0 (Business Central 20.0 (2022 release wave 1)), you have the option to include your Document Creator report layouts as built-in/extension-provided report layouts in your Business Central AL extension.

Please see the "Extension-Provided Layouts" section of our online user manual for more information/instructions.