Amps x Volts x IPM.
If you turn down the WFS on a GMAW you will have to slow down to maintain the puddle. Now the amperage has decreased, but heat input is still as noted in the above formula.
The GMAW process can be modified by feeding less filler metal and increasing arc voltage which typically results in more spatter, slower arc tarvel speeds and will cost more $ to perform. (Eventually you will phase into spray arc transfer provided the correct shielding is employed.)
If you add less filler metal to the puddle of a GTAW, you will have to slow down to allow the joint to fill, but heat input is still as noted in the above formula resulting in an increase of K joules per inch. The type of material being welded may be affected by the "starving of the weld" of filler metal such as many nonferrous materials (i.e.: aluminum).
I think what you mean by "under powered" is less filler metal @ the same amperage for GTAW. This is equates to more heat input and less productivity, this weld cost (much) more $ to perform.
Properly adjusted GTAW or GMAW can provide as much penetration as the power supply/equipment, welding parameters and the material or aplication will allow. I can play with parameters and make either process achieve more or less penetration. Did I mention shielding mediums make a huge difference in penetration patterns? There about 20 macroetch specimens here on the counter in my office using different shielding mediums, electrodes and welding parameters for GMAW, GTAW and FCAW on a variety of materials including disimilar metals joined by FRW. Also have a multitude of macrophotographs of weld cross sections. I think these are what you should look at to "see" what happens when you make adjustments as noted in your post. See if you can get your hands on these types of specimens.
My question to you, why would you want to perform a weld that would cost more $$ to perform. Just my curiosty. It sounds like the physics of welding have really caught your attention. That's very good.
I think that I understand what you are saying: If you do not have the right equipment to weld a particular joint, (in other words a low amperage GTAW or GMAW power source to weld a thick section) you will have no possibility to weld it with the GMAW process, but with some creative welding, should be able to weld it with the GTAW. Is this right?
I believe the answer is yes and no. It is so that in the case of an under-powered GMAW power source, you would probably have a lower range of possibilities than with an underpowered GTAW power source. (The big thing here is however how you define the power source as under powered!) It is however incorrect to assume that you can weld anything with GTAW by just "slowing down". Eventually the energy conducted away through the base metal will equal the energy supplied by the arc. At this point, you will also have no penetration with GTAW. This situation is easily achieved when welding something like Copper.
Something else to keep in mind is that the process efficiency of a process like GMAW is generally higher than is the case for GTAW. This means that GTAW has a disadvantage even before considdering any other parameters.
Hope this is what you had in mind.
Regards
Niekie Jooste