Presumably the server won't let a locked chest be broken.
I imagine it'll disappear for a second in the client (as the client doesn't run the mods) but will reappear, like when you get the reappearing block bug.
Like maybe the square of 8 wooden planks, with a diamond in there to make the chest lockable. Then a key made from two iron bars and a diamond (diamond used in both to keep lockable chests rarer).
Isn't mining the whole point of the game though? What makes it a game? Otherwise you might as well just make a single player map with all the minerals on the surface.