On 5 August 1862 Secretary Stanton ordered that captured arms which were not suitable for issue to volunteer regiments be repaired and "put in order" by the arsenals for issue to the militia. This is one indication that the Federals had a system for recovering arms, refurbishing them, and issuing them. What I have not seen is anything to indicate that the Federals were marking the refurbished weapons like the Confederates were doing.
Regards,
Don Dixon