I spoke to some electrical engineers a few weeks back in depth and they were assuring me that if resistance of the system is unchanging
If.
Plenty of methods of changing the resistance of the system.
Some videos I've seen of small variable dc switch power supplies being used to electrolysis, would have two knobs for current and voltage. You could set one of them, and the other would automatically adjust in accordance to any changing resistance in the system.
To some extent it can work, but as I explained earlier, when you change the voltage you risk reactions that occur won't be the ones you want. In the case of some simple systems (like water electrolysis) increasing voltage can speed up the reaction, in other systems it will start another, unwanted reactions.
Now, I'm no electricity expert, to be clear. When you talk about well defined potentials, how does this relate to voltage and current? Certain reactions happen at certain current densities? Or certain reactions happen at certain voltages?
Which reaction takes place depends on the voltage, not on the current density.
I read some literature somewhere that stated reduction of a specific organic molecule(which I cannot for the life of me remember), occurs readily at 200mA per cm^2 of cathode area, where as at 100mA per cm^2 the reaction does not occur at all. You're saying that current doesn't effect the reaction itself, but only the speed?
Hard to comment on not seeing the context. In general current density should not matter, 100 mA/cm
2 should be just twice slower than 200 mA/cm
2. But perhaps to increase the current density they had to change the potential applied and for some reasons it was easier to control the system measuring the current, not the potential.
Is there a specific 'potential' that electroplating can occur, and a reaction not, or a specific potential where a reaction occurs, but electroplating doesn't? Will a metal ion automatically plate to the cathode if it is reduced regardless of the potential?
Good recipes should contain information about the potential that should be applied. Some recipes will not give this information, but the solution composition is selected in such a way side reactions are not interfering (much), so as long as the voltage is high enough to keep the current flowing and low enough gases don't evolve, the main reaction is the one dominating the solution. Recipes are often designed in such a way they are relatively fool proof, but even then quality of the surface can depend on the potential applied.
Sorry, this is a very wide subject, and while I know a little bit I am far from being an expert. There are thick books on the subject, but I suggest you at least try to assimilate Phys101 and GenChem101 level of electricity and redox reactions.