The critical part is the insulating tubes. Do NOT leave those out. If the originals have become damaged, I would urge you to go get some small diameter soda straws of the right diameter and see if you can wrap the bolts with the plastic straws and then use the damaged cardboard/fiber sleeves which would then become spacers. If you can't find small diam straws, maybe you can slit too-big ones and still wrap the bolts.
All my reading about transformers says the laminations are supposed to be insulated from each other. If you run the new bolts through the corner holes with no spacers, the sawing action of the threads could easily wear away the lacquer coating on the inside of the holes. With no spacer nor insulator in there you could short out laminations with the naked bolt. I can't tell you what the exact effects might be but they are almost certainly not good.
And by the way, when it comes time to cinch down the mounting nuts and then the ground lug(s) on those tranny bolts, be aware that ordinary generic hardware-store bolts, especially long ones like you have, are made with soft, crappy steel to make rolling out so many threads easier. That means you can and will shear off those bolts should you overtighten them rather easier than with the originals. That would suck, to use the technical term.
Just trying to keep you out of the soup.