  We show that orbital currents can describe the transport of orbital magnetic
moments of Bloch states in models where the formalism based on valley current
is not applicable. As a case study, we consider Kekul\'e distorted graphene. We
begin by analyzing the band structure in detail and obtain the orbital magnetic
moment operator for this model within the framework of the modern theory of
magnetism. Despite the simultaneous presence of time-reversal and
spatial-inversion symmetries, such operator may be defined, although its
expectation value at a given energy is zero. Nevertheless, its presence can be
exposed by the application of an external magnetic field. We then proceed to
study the transport of these quantities. In the Kekul\'e-$O$ distorted graphene
model, the strong coupling between different valleys prevents the definition of
a bulk valley current. However, the formalism of the orbital Hall effect
together with the non-Abelian description of the magnetic moment operator can
be directly applied to describe its transport in these types of models. We show
that the Kekul\'e-$O$ distorted graphene model exhibits an orbital Hall
insulating plateau whose height is inversely proportional to the energy band
gap produced by intervalley coupling. Our results strengthen the perspective of
using the orbital Hall effect formalism as a preferable alternative to the
valley Hall effect
