Flow of current in open circuit If we place a bunch of positively charged particles on one side of a conducting wire and a bunch of negatively charged particles on its other side, the situation will be analogous to a battery. Will then current flow in the open conductor for a small amount of time until the whole positively charged particle gets neutralized?

OK, current flow is possible. But can we create a steady current in this way?
 A: A charged conductor has a potential $V$ that depends on the amount of charge carried and on the geometry of the conductor. In general, when two conductors with different potentials are connected with a conducting wire, a transient current passes from the body with higher potential to that with lower potential. The current persists till the potential difference drops to zero, and this usually takes a very short duration of time.
If the two conductors initially have equal and opposite charges, zero potential difference is obtained when both conductors are neutralized. 
Edit:
Yes it is practically possible: two conductors having the same charge with an opposite sign actually form a capacitor by definition, and when we introduce a resistance into the circuit, the schematic representation becomes:

Our job is to find suitable values for $C$ and $R$ to extend the discharge duration as long as possible.
We can apply Kirchoff's voltage law and solve for the current as a function of time, we get:$$I=\frac{V}{R} e^{-\frac{t}{R.C}}$$ 
Where $V$ is the initial voltage. Current decays to practically zero at $t=5R.C$, where $t$ is in seconds, $R$ in ohms, and $C$ in Farads. So, a $1 M\Omega$ resistor and a few $\mu F$ capacitor can create a current that persists for quite a few seconds.
