I say YES!
Sure, they can wear armour and then use their flesh mask to cover it up. This will protect their tender bellies if someone figures out their catch and tagets those areas.
A good point. Armor would benefit them if their Catch is satisfied, even if it wouldn't normally have any benefit beyond their Toughness.
EDIT: I think it'd be pretty rare though. Most physically-powerful supernaturals, especially predators of humans, seem to be arrogant about their superiority over mortal humans. At the very least, one would expect Red Court vampires to wear armor much less often than humans, since the benefit would be much less/much more situational.
If they want full body protection from holy weapons, they'll have a harder time customizing that armour, I think. They'd be better off wearing the armour OVER their flesh mask...but then they'd have ill-fitting armour as soon as the flesh mask dissolves...
Yeah, that would be tricky. And while it would protect them from being burned-on-contact by holy water or characters with Holy Touch, I don't think it would stop the repelling effect of faith (as Harry does with his pentacle); since that doesn't require physical contact, physical armor shouldn't help.
I don't know about sunlight: does it actually have to touch their skin? I think I'd say that it still affects them somewhat -- if they can see, their eyes must be exposed to light by the armor -- but maybe not as badly as an unprotected vampire.
EDIT: Maybe they would just be Compelled (irresistibly since they're negative-refresh) to flee the sunlight, but not actually burned unless they were stuck with no way out for a really long period, in which case they might be blinded.