Hello Marc
I dont know what they do with these wreckages ?
I think that they were recycled as you say-Anyway the fact that they were exposed gave the good opportunity to have a lot of photos and postcards of ww1 german aircraft ,(and incidentally useful for crash file challenge..

)
here is the site of Jean Marie Picquart with(among a lot of interesting photos)
you can see captured german aircraft exposed at Nancy
Avions exposs Nancy
Have a good WE
Cordialement
Bruno