Does the Higgs Boson have a superposition? 
*

*Do particles with mass have a Higgs boson in their make up? 

*and if so, when the particle is as an electron and is a wave going unobserved through both slits, is it carrying a Higgs in the same state?
 A: 
Do particles with mass have a Higgs boson in their make up?

Not in the way you seem to imagine it.  The Higgs boson is an excitation of the Higgs field, an elementary  particle like all other particles in the standard model..  It is the Higgs field that gives mass to elementary particles in the table, including the Higgs boson itself.

and if so, when the particle is as an electron and is a wave going unobserved through both slits, is it carrying a Higgs in the same state?

The wave nature of the electron is a probability density wave, not a mass/energy wave to be carrying anything. As in the first question, the electron is an elementary particle and is not composed out of anything else, that is what "elementary" means.
Composite particles, like the proton, can be mathematically modeled with exchange diagrams and in principle all elementary particles in the table can be in some loops in the Feynman diagrams describing a proton. As the Higgs boson is only  interacting with the electroweak sector, its contribution to the soup is infinitesimal due to the small value of the weak and electromagnetic  coupling constants and its large mass, and is never considered in the description of a proton.
