can I create an SSRS group without adding the group to the box itself and without using Active Directory?
There are a couple of courses of action for you:


If you're friendly with your Windows Admin, I'd thoughtfully think out some AD Groups and then present them to the admin and ask them to be created (in whatever workflow you have). 
From there you can assign permissions on the individual folders by these groups. Click on the folder, then click on Properties.





On the left you will see "Security," click that. Then click "Edit
Item Security." You may get a dialog that tells you that the item
currently inherits from parent. You may need to wait for a bit before
this completes, but be patient.





If successful you will have checkboxes next to the principles already
with access. From here choose "New Role Assignment"





Now you can add your AD Group in the next page and assign it the permissions necessary. Try with DOMAIN\GroupName




Obviously this will be much easier if you have AD groups, but if you can't get that, then you can do this with individual domain users. That would be a management nightmare?