Can the merge based on categories work with contacts in an Outlook public folder?

Yes it can.

EmailMerge PRO/Standard Version 3.x and EmailMerge PRO/Standard Version 2.x
While selecting contact source in Wizard, check the check box to include public folders.

EmailMerge Std Version 1.x / EmailMerge Pro version 1.x
At step 2 of the EmailMerge Wizard click the Choose another Folder button and use the screen that opens to select the folder that you want.