soldiers were trained where their regiment was raised,
Depends. In the Confederacy after conscription was instituted (Spring 1862) conscripts were supposed to be trained at "Camps of Instruction" and were then to be assigned to existing regiments where needed.
Many potential conscripts though were allowed to volunteer and I assume these went straight to regiments raised in their general neighborhoods or into newly formed regiments.
Also many "true conscripts" deserted at the first opportunity (including a G Grandfather of mine)and went home to become "mossbacks" so I would assume that relatively few of those trained at these "Camps of Instruction" actually saw combat.