Those pedals are designed for straps / clips and I would not hesitate to convert that bike with the adjunct that one does no harm to the frame.

I was at the bike co-op yesterday and a fellow was eyeing up a handbuilt Ron Cooper with the intent to convert it into a beater fixed gear.



When I told him what the bike was and how much it was worth he agreed that this would have been wrong and if things work out I will soon be the owner of a gorgeous Cooper racing bike.