Actually no. For example, consider a *scalar* potential field associated with an electric field in space.
To put it in terms of symbols, consider two frames R1 and R2. A scalar field may be defined in R1 as 'a*R1_x**2', where a is a normal Symbol, while R1_x is a CoordinateSym. Since R1_x can be expressed in terms of R2_x, R2_y and R2_z, the given field's expression will change when expressed in R2.
Having a new class will only complicate matters, since no 'extra' functionality is needed- all I need to detect are CoordinateSyms among the atoms of the expression, and substitute them accordingly. I hope things are clearer now?