A dragonborn warforged would be a either a Medium construct (dragonblood, living construct) or a Medium humanoid (dragonblood, living construct), the rules (RotD page 8 and 10) contradict each other. Regardless, most of a warforged's natural abilities are derived from the living construct subtype (ECS page 23). They lose composite plating (thereby no longer qualifying for "Body" feats technically), light fortification, and natural slam attack.
However, to hear the Platinum Dragon's call (RotD page 8) is impossible since the deities of Eberron (and Bahamut is a constellation) do not speak to their worshippers. Divine power is garnered from faith rather from the gods themselves (Faiths of Eberron, page 7). Also, warforged cannot complete the Rite of Rebirth since they cannot sleep (RotD page 8).
An interesting exercise in rules, ultimately up to the DM of the campaign.