What happens if a dependent current source does not dissipate/generate energy?
how do we decide whether Voltage Drop on current source is 0

In this circuit you know it is not 0 because there is a voltage source connected in parallel with the CCCS.
In another circuit you would simply solve the circuit, by mesh or nodal analysis or whatever other method you like, and from that find the voltage across the current source the same way you would find the voltage between any other two nodes.

should i assume that dependent current sources will behave like open switch as well?

You should assume it produces a current equal to \$\alpha\$ times the current in the controlling branch, and let that determine how it interacts with the rest of the circuit.