While the copper cases did cause some problems, it was wildly overblown, mostly by the Army itself wanting to blame a technical feature instead of admitting that poor tactics and worse command decisions caused them to get their butts kicked a number of times. And whoo boy does history repeat itself!
I, of course, had no access to the original ammo, but one time I ran a test firing 60 rounds of BP cartridges in an original Trapdoor carbine, firing as fast as I could. Fired brass cases got kicked out just as easily after the last shot as the first.
No question that disrespect for your enemy will lead to bad decisions and tactics. Not just Custer. If Crook had not had twice as many troops and auxilliaries, including Crow and Snake scouts, and a bit of luck, Custer would have been a footnote. As it was, although Crook claimed victory at the Rosebud because he held the battlefield, his troops had expended around 50,000 rounds of ammo, and he had wounded to care for. His subsequent tail chase of the Sioux wound up with little to show for it.
I have found no reports of jammed rifles due to the copper-cased ammo in Crook's command, however.