Could be done, but it'd be tricky.
Firstly you'd have to assume everyone has everything that the save-file-provider has used in the picture. If they have a model you don't, you'll obviously have missing stuff.
Secondly, just because you have the models in one spot (i'm not 100% sure about this), doesn't mean it'll work. If they have a model in their legacy addons and you have it in your garrysmod/models folder, it may not work.
So, it indeed is possible, but you'd probably have to let (when you give out the save) exactly what models and materials are in the scene.