I did a test. Opened a PDF file saved from Photoshop which has the sRGB profile name saved in the metadata (don't know if the actual profile is embedded or not). Opened side by side, one window with Acrobat Reader, next to another window with Acrobat Pro. And the Acrobat Reader looks very different in they grays than the Acrobat Pro. So I assume that Acrobat Reader is not color managed.
Adobe Acrobat Reader indeed supports color management. If the documents look different, it is because the color preferences and/or viewing mode (such as overprint preview) are set differently.
(Also, FWIW, you should not try to have parallel installations of Reader and Acrobat or multiple versions of same of different releases on a single system. It is a recipe for “issues.”)