Geometry Problem

No

Because AD is parallel to BE.....then  because CE  is a transversal cutting  parallel lines, angle ADC  = angle BEC

But angle ACD  >  angle BCE

So  in the two triangles

ADC + ACD  + CAD  =  BEC  + BCE +  CBE

ACD  +  CAD  =  BCE  + CBE

Since  angle ACD  > angle BCE, then angle  CAD  must be  <  angle CBE

The only way that angle CAB = angle CBE  is  if A is on  BC