Depends where you draw the line on something being designer a bit, but if we're including luxury brands in general, then essentially yes in most cases.

If someone cares about their appearance and they have enough wealth to not need to worry about economising, they will be wearing something close to the best versions of a given item of clothing that they (or their stylist) can get their hands on.

It doesn't have to be flashy (and increasingly the goal is to not be flashy), you can spend hundreds, even thousands on a plain black t-shirt. If someone wealthy wants a black tee, it's almost certainly gonna be one of those and not one from a supermarket.

Is the difference in value equivalent to the difference in quality? No of course not, the prerequisite is not needing to worry about the cost. There's no value to them in shopping around for a deal and/or compromising due to cost, they just want the best available, and that's it.

Now there's the demographic of wealthy people who genuinely don't give a shit what they look like, and instead dress like eccentric geography teachers, but even then, I don't think they're getting their clobber from a Walmart.

Edit: typo