Although having both the anode and cathode in one beaker is less usual for galvanic cell, more common for voltaic cells, but if the electrolyte is the same, then yes, it is possible, whether you get a reading or not will depend whether you have correctly connected your electrodes to the -/+ on your voltmeter, if you connected it wrong, you might get a negative voltage-i.e. the voltmeter deflects to less than zero Vs, if this occurs, you know you've made an error, and will most likely have to switch the connections to get a voltage,
Don't confuse things, voltage is basically electric potential energy per unit charge, so it is the NET movement of electrons through the external circuit that you connect with wires to the voltmeter, that creates the reading on the voltmeter, while displacement is essentially referring to the redox reactions-that allows anode become oxidised, convert from metal to metal ions into solutions, cathode being reduced, and the ions making up the electrolyte solution essentially(cations and anions) serving as spectator ions, like in a salt bridge, to preserve ion neutrality and allow the continuous flow of electricity.
Essentially a galvanic cell produces electricity by
1)at anode-oxidation reaction liberates electrons, flow out of the metal of the electrode and into the external circuit
2)these electrons flow through the metallic conductor(wires) of the external circuit to the cathode
3)The reaction at cathode(reduction consumes these electrons)
4)ions migrate through the solution and connecting salt bridge-can be ignored if you want a common solution-to maintain electrical neutrality
Remember for pracs-you must remember validity, reliability, accuracy, how to improve these aspects and evaluate these aspects in reference to prac, remember to draw up a diagram labelled if required, areas for improvement, sources of error-why different from theoretical value(I.e. not performed under standard conditions), independent/dependent/controlled variables may need to be identified-any more questions, welcome to pm me-and best of luck for your upcoming prac
hope my reply helped