[Gameplay] Zoe and Mark/Dash

If you use Zoe's W (Spell Thief) to pick up Mark (the snowball) in ARAM, you can fire the snowball as normal. If you hit someone, you get Dash. If you Dash in, you get your normal W back, but if you let the mark expire without dashing, Zoe's W remains Mark/Dash and goes on that spell's normal 80 second cooldown. Is this intended behavior? There's nothing to directly compare it to, since Mark/Dash is the only two-part summoner spell, but other summoners and actives don't go on cooldown.

I died before the 80 seconds were up, so I wasn't able to verify if my W would return to being Spell Thief or remain Mark/Dash once the cooldown was over.