Andrew,
While it is not shown in the main properties for a project, each project does have it's own calendar, so yes you would be able to set each project depending on which location the project is lead by.
To access the calendar, type 'calendar' into the search at the top of the project page. You should then see the calendar, select edit and the then calendar settings which should open up a screen the same as any other calendar setting page but will only be for that project.
Regards,
Phil