Deleting a character with 400 Crafting
If you delete a char you remove everything that char has. So no, you shouldn’t keep the armorsmithing.
It would be the same as getting 1 char with max level crafting and then giving it to a fresh char.
Suggestion: a character expansion slot is pretty cheap with the exchange rates lately.
If you think you might want armorsmithing 400 but don’t want to play the character, just keep it as a dedicated crafter/banker, and play in a new slot.
Thanks for the suggestions and information.