Yes, it will require a macro solution.
Before that can be designed, you need to specify what kind of check box you're using. Is it a content control, a legacy form field, or an ActiveX control?
A post that shows how to work with ActiveX controls (in that case, option buttons) is at https://answers.microsoft.com/en-us/msoffice/forum/all/change-the-cell-shade-color-when-selecting-the. However, if you don't already use ActiveX checkboxes, I'd advise you to avoid them. If the document needs to be used by Word for Mac or by Word for Windows before Office 2010, stick to legacy form fields.
Reply here to get sample code.