treacarr - You do not need to enlist in any challenges/wars/etc. With Ghosts your clan is auto-enlisted. The only exception is with Diamond Division clan wars where you have to opt into either the Diamond Division or the Bronze-Platinum division as well as specify which timezone your clan will participate in.
To manage your clan you will need the app as it is the only way to manage most items. After that you don't technically need the app aside from to see stats and set your target for the clan war though you aren't required to do that in order to participate. However, without the app there hasn't really been a good way to view any of this information either.
If you want to view all this on a website (only view, can't edit), then you can visit http://www.codcp.com which allows you to sync data for your clan, your roster, and your rosters stats. It also provides real-time clan war data to view during a clan war. To see a sample, clan you can view my clan at http://www.codcp.com/c/1000/ which has the full roster and data history implemented. There is no clan war currently in progress so I can't really show what that looks like.
As Tracy said, you can still level up your clan and earn XP but it will be more helpful for you if you know what your goal is in a clan (the war is the best way to earn XP assuming you can place 1st, 2nd, or 3rd...especially for smaller clans who don't have as many people playing together.