Frankly the Union would never be able to adopt such a weapon given their starting circumstances.
Firstly, the limited arms manufacturing facilities in the United States would have to retool manufacturing and retest for proof of any new weapon. Given the Ferguson’s stock had a tendency to snap around the lock (was never intended as a mass issue but rather a specialist light infantry weapon), it would have rejected right off the bat.
Secondly, this is the age of the rifled-musket. To begin using the Ferguson rifle would be seen as backwards, as military theorists proclaimed the rifle musket to have a far greater range of the rifles musket.
But let’s toss all objections and play with this hypothetical scenario. The Ferguson rifle would never be available in time for First Battle of Bull Run. There would certainly be shortages in available Ferguson rifles and as a result see mixed arms in most Union armies.
The Ferguson rifle would certainly provide mixed results for the Union. On one hand the Ferguson more than doubles Union firepower and could definitely shoot up any Confederate assault.
On the other hand, early ACW units displayed poor fire discipline. Reading the OR reports, it frequently appears that a regiment marched out into the battle, shot off all its ammo, and was then forced to either retire from the field, or to stand and take fire while waiting for a re-supply.
Another disadvantage would be the extreme logistical burden the Ferguson rifles place on Union logistics. When Grant began his Overland Campaign in 1864, there was one draft animal for every three soldiers. Added ammunition trains would have added the requirement for security for the cargo and forage for the draft animals that was already a problem for the Union Army. An entire division or two worth of regiments could be used up in providing security and providing and distributing ammunition.