No, electron would not be deflected if `vec(v) and vec(B)` are in the same direction. Further the electron would not be deflected if in addition to magnetic field, there is electric field present. The two deflecting forces may cancel the effect of each other, giving net Lornetz Force zero
i.e., `q vec(E) + q (vec(V) xx vec(B)) = 0`
If both `vec(E) and vec(B)` are present then `vec(v) and vec(B)` can make any angle between them but the `vec(E)` should be perpendicular both to `vec(v) and vec(B)`. As a special case you can say that all three vectors should be perpendicular for no deflection of the charge
