I would say this depends on the electrode that is used. Some electrodes may charge when submerged in electrolyte, therefore it is important to discharge them before starting an experiment as this can reveal strange current values at the beginning of the experiment. You can short circuit the electrode with the counter electrode until the current reaches a steady state value around 0Ampere, preferably in the nano Ampere region for electrodes of around 1cm².
This equilibration can be short or very long but generally i would indeed say that at least 10 minutes is needed, while sparging with the gas you are using.
Hope this helps. If anyone disagrees please comment.
Yes, that depends on the electrode materials. If there have large surface area and it may take some time to get the equilibrium. Generally, 10-30 min is enough and 60 min if you have plenty of time to wait.