Interesting question…. My first answer is no, it wouldn’t because I’m more interested in what’s in the bottle not necessarily how it looks.
My follow up is putting my public health hat on and wondering how the enclosure fared on the road from bottling to sitting on a shelf somewhere. Of course boxes would prevent most things from settling in the space where the cork sits, and it’s easy to see if someone has tinkered with the cork or contents if there’s an in-tact enclosure. It’s not a problem until it’s a problem. That’s why we now have sealed and shrink wrapped over the counter medications in child-proof containers.
That being said, if I liked the wine, it probably wouldn’t really bother me at all.