It seems that it is possible to "assign" a column vector with a row vector of the same size without actually changing the dimensions.
For example,
...
Vector3d v(1, 2,3);
RowVector3d w(4,5,6);
v = w;
...

After these codes, v is still the column vector.
Am I correct?

The type doesn't change.

Yes, we allow for an implicit transposition in this case.