Patching is good only if there are very few holes (5 can be too many) and that they are far apart. FInding them closely bunched means that the rubber coating is fast breaking apart, so patching will just be a very temporary remedy.
A deteriorating curtain will soon have other places to break and form holes on, than the ones patched. Check if the coating is still supple. Any dryness or flaking means that the vulcanised coating is going and will soon be gone.
Good curtains can be patched. I have patched my shutters with black fabric paint (the thick, 'embossed' type) for years, and the patches are still good.
Most IIIc have better, more durable shutter cloth than the later IIIf or IIIg. I've 2 IIIc from the late 1940s whose shutters are still original and supple. In contrast, almost every IIIf I've seen have dried crumbling shutters.