If you do not have space in your inventory, you'll get the message: "You found a shard emanating magical energy as you were training, but there was no space in your inventory to take it." Once there is a free space, the shard will be obtained. It is possible to receive a shard while training the skill while Dungeoneering, and it would be sent to your bank unless it is full, in which case you get the message: "You found a shard emanating magical energy as you were training, but there was no space in your bank to take it."