is this an important quest? Should I be worried if I can't finish it?No, it's not an important quest, and it doesn't really matter if you don't finish it.
I'm not sure whether or not Gungnir is one of the artifacts that reappears after the area respawns; I rather think it is, but I'm not sure.
But in any case, there's an easier way. Download a copy of Klar's Black Chests program and run it. That will reset all the black chests, so that not only will you get another edition of Gungnir, you will get all the artifacts that you missed in the early stages of the game when your party was either unable to reach the chests or unable to open tham safely. 
