It can.  This was one recipe I passed on to several who've given it great reviews.

Shrimp takes only minutes to cook.  I'd use peeled and deveined 21-25s and tuck them in the mixture after it has been removed from the head.  The residual heat will cook it without overcooking.

Dirty rice, from what I remember making, was a side rice dish with minced chicken gizzards and livers.
Vern, got a recipe of what you're talking about?  I'm interested.