Can you fix a blind above or onto a curtain track?

I live in MOD property, therefore am reluctant to make too many changes to fixtures and fittings. The current curtain tracks are fixed onto the wall, and the screws have been painted over, meaning it would be quite difficult to remove them without damaging the wall or the tracks, which i'd then need to replace when I move. Is there any way to fix roller/venetian or roman blinds above/below or on the track without it looking daft or ruining existing fittings?