Can the potential difference produced in Van De Graff generator used to generate electric current? If this machine can build up high voltages of the order of millions of volts, can we use this voltage to generate a current of electrons? The building up of potential difference can result in an electric field. Can we not use this electric field to generate current?
 A: The quick answer to your question is "yes".
However, there may be a problem. When you ask, "Can we not use this electric field to generate current?" you have not clearly defined the amount of current you might want generated. 
Van de Graaff generators are not notably efficient, even among other electrostatic generators such as a Wilmshurst machine. The charge transfer mechanism (induced charge on a moving belt) simply does not move many electrons per second. The great advantage of the Van de Graaff is that it can store those electrons without much leakage, allowing a high voltage to build up. See http://hyperphysics.phy-astr.gsu.edu/hbase/electric/vandeg.html, and note "discharges from the Van de Graaff do not represent a serious shock hazard since the currents attainable are so small."
So, although you can use a Van de Graaff to generate current, you can't generate much.
A: Yes, of course.  The "building up of potential difference" is alway accross some inevitable capacitance.  Charge on a capacitor is energy, which can be released as voltage x current x time.
Think of it another way.  The generator obviously has to produce current to charge up the capacitance, so this same current could be drained by a load and the voltage kept constant instead.
A: Well, Robert Van de Graaff (note spelling) founded a company to make accelerators (electron and ion) called High Voltage Engineering.  With no beam current, the terminal is kept at constant potential when the net charge going up the belt to the terminal is balanced by the charge flowing down the column (precision resistor chain) and out the corona points (if so equipped).
My HVE EN tandem accelerator stills runs everyday after 52 years.
So, yes, you get a current flowing.
Sparking is bad form, and bad for the accelerator, but we want to do real science, not make sparks...
A: The spark is the resulting current.  Once enough voltage is generated to arc the gap, a current is generated and the voltage is changed with the exchange. 
