i just tested this out myself with a lesser known artist that is in fact on iTunes and Apple Music and their name was greyed out on my Music app for a particular album. Went to their artist page and added the album to my Library because iCloud Music Library wasn't recognizing that it was for some reason. The artist name turned red in my library for that album but when trying to click it, it still does not take me to their page.
Roughly around 700 albums on my iPhone and every single test I've done in the last hour or two works exactly to my findings.
The only greyed out artist "button" are on artists who aren't available on iTunes. And the only time a red artist "button" doesn't work is if the album you're viewing at the time isn't available on iTunes.
The rest of the time it takes me to the artist page.
100% every time this is the behaviour I have for every artist and album I've gone through so far (I've tested a mix of well known and not very known at all artists and albums)