Reverse saturation current in a BJT: active and reverse active modes
The saturation current of a PN junction, as you correctly said, depends on the cross sectional area of the junction itself.

In fact, if you look at a datasheet \$ I_{CBO} \gg I_{EBO} \$, confirming your idea.

Moreover, Sedra/Smith (I'm looking at the 6th edition, page 361) says:


  The structure in Fig. 6.7 indicates also that the CBJ has a much larger area than the EBJ.


As you said, the collector-base junction (CBJ) has a larger cross sectional area than the emitter-base junction (EBJ).
They then continue:


  Thus the CB diode \$ D_C \$ has a saturation current \$ I_{SC} \$ that is much larger than the saturation current of the EB diode \$ D_E \$.
  Tipically, \$ I_{SC} \$ is 10 to 100 times larger than \$ I_{SE} \$.