Yes EIGRP will converge to the next successor (feasible successor, if any). Feasible successor is the backup route (if any exists) that eigrp calculates and stores in its topology table. For a route to be a feasible successor it needs to satisfy the feasibility condition.
More on this can be read at the Cisco website.
Also, if a route cannot be a feasible successor, and when the primary fails, eigrp will query its neighbors for an alternate route, and if one exists, the network will converge through that route.
So the answer is yes, EIGRP will help in reachability of packets from site B to A, through site D.
Sankar Nair
UC Solutions Architect
Pacific Northwest | CDW
CCIE Collaboration #17135 Emeritus