In the process of inverse melting, a crystalline solid solution on cooling becomes less energetically stable than the isocompositional undercooled liquid or amorphous phase. Due to this, the crystal may transform polymorphously to the amorphous or liquid phase. A thermodynamic requirement for this process is the presence of two crossing points of the free energy curves G(T) of the crystalline and liquid or amorphous phases. Fulfillment of the thermodynamic requirement is however not a sufficient criterion for inverse melting to occur. In the present work the question posed in the title is addressed from both a thermodynamic as well as a kinetic standpoint. It is shown that in bcc phases which would otherwise undergo inverse melting, the presence of an energetically favorable B2 phase may prevent inverse melting due to its fast ordering kinetics. This imposes an e/a limit to the occurrence of inverse melting.