My argument: Bread is leavened and whose basic mixture is flour or meal. (Usually baked, but so are most cakes so I’ll leave this as moot.)
If a cake can meet those requirements, Yes, it would be a bread.
Otherwise, it would be a breadlike food. In the cake definition it uses a “breadlike food” probably due to to the latter half of the statement “often unleavened”. This would lead me to presume that most cakes, while breadlike, do not meet the requirements. It’d be more reasonable to make a statement on the majority (breadlike) than minority (Bread).