The assumptions/requirements of the basic BSP analysis are that you have a random sample from a single panmictic population (the geographical species distribution, range sizes, dispersal directions/distances, etc, themselves are not relevant,
unless they impact on either of these two assumptions/requirements). So, if there is any population subdivision/structure that would influence mating/random sampling, then, yes, the assumptions/requirements of the basic BSP analysis will be violated (which may or may not make any inferences from it unreliable, depending on the extent and nature of those violations).
A sensible approach would be to first perform some separate population genetic and species delimitation analyses on your molecular data to see if there is any evidence that your apparently single species consists of two (or more) subpopulations/taxa. There are also methods implemented in BEAST that allow skyline analyses when there is population subdivision/structure.