Answer
No. Yes.
Work Step by Step
If exactly one force acts on an object, the net force is nonzero, so by Newton’s second law, the object must be accelerating.
It is possible for the object to have zero velocity, but only momentarily. The classic example is a ball thrown straight upward. At the top if its flight, its velocity is zero but it has the same nonzero acceleration the whole time, directed downward with magnitude g.