Nala,
The quiver will be harder on the broadhead edges than the broadhead edges will be on the quiver.
I've got a machine stitched Hill quiver from the 60's that's had thousands of broadheads drawn from it and it's in great shape.
Hunting with a shoulder quiver is a little harder on broadhead edges than a bowquiver is. You just need to establish a routine of inspecting and touching up your broadheads each day.
It's really not as bad as you might think, though.
I never have used the leather broadhead covers, but think they could be a little unhandy.