Yes, it should be installed AND active in the Addon Manager. If that is already your solution, you can be happy with it.
But I think Alphatango2 referred to the scenery library that you can access via "World => Scenery library" in your P3d menu. You can also see those entries in your scenery.cfg file, (unless the xml method is used, that registers an addon "from outside"). But in the scenery library, you can see both entries: classic via scenery.cfg and via "the new" xml integration. Actually I don't know which method FSDT uses, because it has always been automatic. But it is possible to do both manually, if they disappear.
I don't know how much knoledge you have about the P3d structure. But in order to make a scenery work, you have to "register" the files within the simulator, so that it detects it to show up when you go there. If that internal registration is missing for any reason, only the files are there, but they aren't shown in the sim. You basically registrate the folder, that has at least a subfolder called "scenery", and most of the time another one called "texture". So, adding the FSDT sceneries manually (once the registration entry has disappeared for any reason) is no problem, because you can easily find the folders with the scenery name that have exactly those 2 subfolders. For example, within the FSDT folder "Addon manager / FSDreamteam", I can find a folder called KCLT, and this one has 2 subfolders: scenery and texture. So the folder "KCLT" is the one you would browse to when you wanted to add it manually in your scenery library.
BUT: My problem with GSX is, that GSX is no scenery, but a tool. It doesn't have a folder within "Addon manager / FSDreamteam", neither does it have a scenery and texture subfolder (probably), at least not one that act like sceneries. That's why I didn't understand how to add GSX to a scenery library.
All this has nothing to do with the Addon Manager itself. This one is an interface created by FSDT to show in a convenient way, which of your addons you've got a licence for, and which of these are installed or activated - and that means "activated" in a sense that the addon manager has detected that you have a licence for the scenery and enables the files to show up in your sim. That doesn't automatically mean that they are registrated in your scenery library, even if the addon manager normally does that for you while installing the product.
So, I don't have any clue, why GSX shows "installed" AND "active" AND the sub menus show up in the sim (under the addon bar), but it simply doesn't want to work for several persons including me.