Formal Charge of Terminal Atoms
Yes, the formal charge at such atoms would be different.  Such atoms, typically found at the at the edge of some crystalline or regular solid, are known as "defects" in the solid.  Because they have an incomplete outer shell and lack a stable bonding configuration (bonding vacancies), they usually exist as a radical, anion or cation.  They define an area of extremely high reactivity on the solid's surface and mark the spot where reactions often begin.

Edit: references to charges at defect sites

this link covers inorganic systems, see p.5 for some nice pictures.

this link covers graphene systems, from the "Conclusions" section; "We have performed scanning gate microscopy on graphene and observed such charge inhomogeneity and puddles due to extrinsic doping from possible sources such as metal contacts, graphene edges and surface residues."