Answer: No.
Explanation: If an object moved to produce a vertical line on the velocity-time graph, it would mean that it would move at an infinite speed with no change in time. Nothing moves at an infinite speed; it is just not possible.
If you wanted to look at it through a calculus lens, acceleration is the derivative of velocity. You can't take the derivative of a vertical tangent line, so the acceleration wouldn't exist. This isn't possible if an object is moving; it has to have either constant acceleration or a non-zero acceleration.