"Repeating rifles and the ACW." Topic

Had the Union army been able to substantially arm even one army with repeaters (Spencers or Henrys), would the supply system have been able to keep up during a battle?

yes

Did Wilder's brigade ever have problems in supply? I know he had several different types of rifles in the Brigade. At one point he had Spencers and Colts.

It depends far less on the supply issues than on the training of the men.

There was a common belief that any magazine rifle would encourage the men to waste ammo and this proved true in some actions. Another worry was that officers would lose control of the unit's firing as men just banged away until the magazine was empty and didn't hear commands – that certainly happened, even as late as WW2. To my mind the 2nd is a far more serious problem.

Well trained men would only use the magazine when it was most effective (i.e. at short range when the volume of fire was likely to achieve significant hits and stop the enemy advance) and so ammo supply would be less of a problem.

The other point is that, if you expect to use more ammo, you will change your re-supply procedures to cope. By the stage in the war when these were introduced Union logistics was pretty effective I think.

The Prussians didn't appear to have that problem in 1866, and they didn't carry any more ammo than their Minie armed opponents.

The Prussian Dryse is a breech loader but not a magazine rifle. Obviously it has a faster rate of fire than a muzzle loader but the difference isn't as large as it would be with a magazine.

I also think it safe to assume they were fairly experienced in its use and any problems with ammo supply had been solved as it had been used since 1848.

Feeding and replacing horses was the #1 supply problem, followed by feeding the troops.