Koverall is polyester fabric, as I recall. Dunno that it will accept dye, but poly clothes do come in various colors, so I'd expect that it would. There is an alternative, and that is using a small percentage of pigmented dope in your clear dope.
The result looks exactly like dyed silkspan or silk or whatever the covering is. I've inspected this Barnstormer by Mike Haverly very closely, and there just isn't any way to tell which it is. PLUS, it doesn't fade like most dyes.
Very slightly heavier than dye, but better in most ways, IMO.
Steve