Can i add a All Staff universal security group to Global security group?

Hi
 
I have a site in SharePoint called Health and Safety. 
On our Active directory, we have a global security group called SafeOrg and any staff added to this group, they will be able to see the Health and Safety area in the SharePoint and will be able to access the files.
Also, we have an AllStaff Universal security group and this group contains 150 staff members.
 
I would like all the staff in our organization to have access to this Health and Safety area.
Now if I go to the Active directory – SafeOrg security group - Properties-Member Off
-Click Add and add AllStaff Universal security group into SafeOrg security group- Will this work?
Or do I need to go to Active directory - SafeOrg security group-Properties-Members and add each staff manually?
 
Please suggest what is the best way to add all the staff’s to the SafeOrg group.

Thanks and any help much appreciated