Providing the old concrete path is stable and relatively clean, there is no reason why you cannot pave over the path. If in doubt, break cold path in situ and compact before laying new pathway. To ensure a good adhesion between old and new cement, add some DPA/Polybond to mix.
Because of the additional height, visually the results may not be great and certainly you will need to trowel edges to ensure clean finish. Also achieving neat grass edges will be more difficult.