No you can't, it treats her body like a powerful creature so the mission wouldn't "bug"
You can make Katria's ghost follow you during the quest. Just do everything in Arkngthamz until you reach the end where you have to shoot arrows at the keys to the final gate and instead of finishing the quest, exit through the shallow water channel to the left exit to Skyrim and make sure you shoot her ghost once with daedric arrow and she'll be the BEST archer 'follower' you'll ever get (she can't die).
You can make Katria's ghost follow you during the quest. Just do everything in Arkngthamz until you reach the end where you have to shoot arrows at the keys to the final gate and instead of finishing the quest, exit through the shallow water channel to the left exit to Skyrim and make sure you shoot her ghost once with daedric arrow and she'll be the BEST archer 'follower' you'll ever get (she can't die).