Composition is randomly generated as the item is created. There is no evidence to suggest otherwise, and suggesting it is generated when you pickup is just assumption based on lack of knowledge.
The reason you can't see an items composition when it is on the ground, is you only recieve the ItemID, which matches up to its name in ItemType.dat. Composition, Sockets, Blessed and Enchanted attributes are not part of the item ID, there is no information for them in the item file.
When you pick up an item, you receive another packet, which contains all the extra information for the item. The packet containing the extra information is a 0x3f0 packet. You can only receieve the 0x3f0 packet by picking the item up.