OK to attach Tyvek or any breathable membrane directly to studs?
I'm not an expert on this but based on what I know about breathable membranes in building construction I don't think you would want to have the membrane on the interior side of the OSB or plywood sheeting. I'm also not sure why you would want to do that.
The problem is that these membranes are water-proof but vapor-permeable. With the OSB between the membrane and the weather you're probably going to have moisture issues and probably mold/mildew problems in the OSB or plywood. So you'd be defeating one of the main advantages of the membrane.    

I believe you want to make sure it's attached to the exterior side of the OSB.  

Edit
I'm responding to your comment in my answer so I can include a picture.
Most exterior cladding or siding allows air to circulate under it to solve this problem.


If you install plywood in place of siding over the membrane I do think you will still have the moisture issue. You need a space for air circulation.  

Second edit  

If you attach the membrane to the studs and then cross-batten over the membrane and into the studs and then the plywood/OSB that would give you room for air circulation but structurally I see it causing problems since I don't see the membrane having the structural integrity to properly support the plywood/OSB.