It's not intended to be. It (GFCI) is intended to be suspenders in addition to your belt. If the floor and your feet are dry and you are wearing your Crocs (which I do as a fashion statement, not for protection from spurious currents) you don't need GFCI. It is there for when things go wrong that shouldn't go wrong.Unfortunately it is NOT cheap insurance, it's a false sense of security.
You should do it periodically. Doing it every time you use it cannot, of course hurt and were I brewing once a month checking it each time would indeed be good practice.You should check your GFCI EVERY TIME.........
It's much simpler than what you propose and does not lead to objectionable current in the system. Simply stick one probe of your ohm meter in the grounding conductor hole (round) of an outlet near (can be the same) the one into which the appliance or rig is plugged and touch the other to the brew kettle, stand, sheet metal of the appliance or whatever you are testing. If the impedance is less than 1 Ω clearly your appliance is properly grounded. If you want to get fancy stick one probe of the meter into the earth (round) and the other into the wide slot (after having first verified with the voltmeter or bug that the outlet is wired correctly) of the outlet. This measures the impedance of a round trip from the receptacle to the panel half of which is the impedance of the grounding wire. You can, then, deduct half of what you measure here from what you measure from your appliance.Checking grounding is as simple as having a push button that routes a significant load through the ground from one leg. If the ground carries the load (120 volt load), it works, and will protect you. There are a number of clever ways to do this.
If you measure (appliance to system ground) 1 Ω (don't correct as the fault current has to flow to the fault point through the phase as well as back to the panel through the grounding connector) then it is clear that a phase to grounding conductor (not phase to neutral) fault will draw 120/1 = 120 amperes which is plenty to trip a breaker up to 120 amps. If it is, conversely 4 Ω then the fault current will be 120/4 = 30 amps which will not trip a 50 amp breaker. The grounding circuit in such a case needs attention (remove corrosion, tighten terminal screws etc.). Now note that you are still safe from the POV of the wires in the walls as the phase and grounding conductor are both carrying currents below the level of the protecting breaker. But lots of power is being dissipated in that extra 3 or so ohms of fault. That point will get hot and as it is probably a screw terminal possibly hot enough to start a fire but in a box, not the walls.
As the discussion here is mainly on GFCI's it is pertinent to assume that the poverty in the grounding system might occur by a corroded or loosened grounding ring at the kettle electrode. In this case we might assume that the 3 Ω is across that ring and then suppose a phase to the kettle wall fault. As objectionable current of about 30 amps is flowing across that ring the voltage on the kettle wall will be 90 volts WRT house reference. If you touch the kettle in this case and you are an IEC standard bloke (without your Crocs and wet feet) on a wet slab floor then you might have 90/3000 = 30 mA or more, as in any of the cases which can reduce human impedance below the IEC measurements, leakage through you. This, in a nutshell, is what GFCI is for.
We note again the belt and suspenders aspect of it. We had to have
1)A problem with the grounding system and...
2)A phase to grounding system fault
in order for the GFCI to step in and save the day.