Yes because you'll still get the rewards from the Adventure it just won't mark that portion of the goal complete if you happen to get it WHILE they are on the Adventure. My issue was I got the goal, along with the Forging Excalibam at the same time. I sent them on the Adventure and the next day when I collected from it I got a Mithril. The Mithril portion of the goal wasn't recognized so I had to send them AGAIN hoping I'd get another Mithril, which I did, so both the Forging of Excalibam and this particular goal of "sending the knights/get mithril) ended up completing at the same time as the sword takes 20 hours and the Adventure takes 22 hours. I just got VERY LUCKY that I got that 2nd Mithril on the very next Adventure so it would get recognized.
These are the last 2 goals that pop-up before you have to expand to the Troll King and then Defeat him, as you can't do the last 2 without Forging the Sword first.
I did PM with MHz_ and he was going to have the team look into WHY it hadn't recognized me getting the Mithril in the first place, but since I had already completed the task before he got my original PM, I'm not sure if they'll be able to trace why my goal went wonky. I just hope nobody else has the issue I had, or if they do, they get lucky and have the items needed to immediatly do another Dark Caves Adventure and get another Mithril right away.