Answer
Velocity is generally not, while acceleration is parallel to the electric field.
Work Step by Step
The electric field is the force per charge at a given location in space.
$\vec{\mathrm{E}}$ points in the direction of the force experienced by a positive test charge.
The motion of the proton (positive charge) can be in any direction; it does not necessarily follow the filed lines of the field. As an analogous example, think of a projectile in the gravity field of the earth launched at an angle. Instantaneous velocity changes in time.
The acceleration, however, points in the same direction as the force, which is the same direction as the electric field.
