Could the second situation ever occur? And why yes/no?
There are two properties one can read from a display of electric field lines:
the direction of the field
the strength of the field (up to a constant of proportionality)
The former is tangent to the field line, or some kind of weighted average of the tangents to nearby field lines. This is the property usually invoked to show that they can not cross (can't point in two directions at once, see?). You've more or less defeated that argument.
But let's consider the second property: the local strength of the electric field is inversely proportional to the distance between the lines in this region of space. As your proposed lines swoop towards each other that distance goes to zero with the consequence that the strength of the field increases without bound. Another un-physical conclusion.
You can arrange a physical situation that approximates your drawing by getting very high field strengths in a pinch, but not one in which the drawing is exactly correct.