The FEC burns so efficiently that it would be highly unlikely to oversmoke, virtually any product.
I suppose you could purposely hold cheese,shellfish,fish fillets for many[24] hrs down at a minimum smoke level of around 140*,leave the door cracked partially open,use a smoke stick,stacked around the edge of the firepot.
I've not heard of it, in the years they have been around,but anything is possible.