Considering that the Spencer (and later) carbines had sling rings on the left side, probably not. I did notice in the one view that the cartridges seemed to have "holes" in the back end. Might be for some new-fangled central-fire priming caps, maybe?

Doubt that will ever catch on, hmmm? In point of fact, if you are going to use such things, you better use bullets with a flat point, say, at least .210" on the meplat. Otherwise, you might set off the primer in the cartridge ahead. Such a thing is not a good idea situation in one of those Henry Repeating rifles, with the tubular magazine under the barrel. But in a Spencer, with the magazine in the stock, right next to the shooter's face, it could ruin your whole day! :'(