Just as @Brecht Van Lommel (brecht) said, modifying the ED_operator_editsurfcurve poll function affected other operators as well.

To counter this, I reverted ED_operator_editsurfcurve back to its original state. Changed the poll function in add vertex operator from ED_operator_editcurve to ED_operator_editsurfcurve so that it allows both curves and surfaces.
Next, I modified the ed_editcurve_addvert function to check if the NURBS surface it is operating on is 1-D or not by checking the pntsv attribute of the NURBS object.

At this point, Ctrl + Click works as intended for all curves (included in both Curves and Surfaces) and since the ED_operator_editsurfcurve poll function is back to its original state, other operators which depend on this poll function should work as well.