Without the invite, yewt program dwindles in recruiting and continues their mediocre performance
With the invite, they got money and recruiting
Yewts were invited, at least, because there were no other non-BYU teams left in the west
BYU wasn't invited because, in the PAC's own words, BYU wasn't a good "cultural fit," which was clarified to mean BYU's religious affiliation
The only reason the PAC made that statement is because everyone in the world recognized BYU was the obvious choice from every salient metric.

So yes, the "brand," was elevated because of BYU in the end. No BYU, no expansion, no yewt invite, no yewt success.

But let's be clear, yewts can't really seriously throw around the words "Ute" and "Brand" together without the rest of college sports snickering.