Does calcium has any role in vasoconstriction?
Yes it does, as a matter of fact calcium plays a huge role in muscle contraction, as so in the smooth vascular muscle.
No. Vasoconstriction is a squeezing of the veins. This is like putting your thumb at the end of a garden hose. The constriction of the flow increases the pressure. The water shoots out faster from the hose when your thumb is blocking the way. If the entire hose were to tighten, as in vasoconstriction, the same effect happens. -- From Wikipedia: Vasoconstriction "Generalized vasoconstriction usually results in an increase in systemic blood pressure..."