Yes, you can still use artifact appearances in future World of Warcraft expansions
The bankers in Stormwind have seen some stuff, man. You can just see them chilling on their lunch breaks talking about how the Ashbringer used to be whispered in legends, but now banks are just clogged with Ashbringers. That’s the way the World of Warcraft turns, though, and the good news is that you won’t have to stop looking like you’re swinging around Ashbringer or any other artifact weapon once the next expansion rolls around. Yes, you can transmog that slightly better green weapon to look like a mythical artifact, why not?
Of course, the flip side is whether or not you can even obtain the appearance, and the answer to that is also an affirmative… with two caveats. If you’re hoping to obtain the Mythic keystone appearance or the Mage Tower appearances, unlock those before the next expansion comes out; those will be going away once you can make the challenge trivial. If you’re hoping to just have the normal artifact appearance, though? Don’t fret, it’ll still be there with the next expansion, and on through the next one beyond that.