The reason graphics card don't autodetect RAM is because its not possible for the user to replace. The manufacturer hardcodes the memory configuration into the graphics cards firmware memory. If the manufacturer wants to make a card with double the RAM they swap out the partnumber for the RAM chips and update the memory config in firmware.(Its common to have 2 different memory size variants of the same card). So if you ware to desolder the RAM and put in bigger RAM chips yourself the card would still see the same amount of RAM since that is the amount of RAM the firmware tells it it has, won't try to use RAM that it doesn't know it is there. Or in a worse case if the new RAM chips timings are too different the different RAM might not work at all because the GPU will continue talking to it with timings from the RAM chip it originally came with.
This sort of method of just sticking in more RAM chips and it magically uses them is from the times of Intel 386 PCs. Where RAM did not have any identification on the modules, or you stuck raw RAM chips directly into the motherboard. In that case the BIOS would simply perform a RAM test on bootup that tries using incrementally larger amount of memory and checks at what point data starts getting lost. This is one of the reason why on old PCs you would see a number in KB counting up at boot, then stop at however much memory it found then continue booting, this is the BIOS testing for how much RAM there is. In modern times this is not so simple anymore because not only does the memory controller need to know how much memory is present but it also needs to know what the memory configuration is and what timings it requires. One stick of memory might run at 800MHz with CAS latency of 5 clock cycles, another stick of ram might only be able to run at 600MHz with CAS latency of 5 but might work at 800MHz with a CAS latency of 8 cycles...etc the BIOS needs to know all this to properly configure the memory controller for the correct timings that this exact stick of RAM supports. This is also why it is sometimes problematic when mixing different sticks of RAM in dual channel mode, the timings might be too different for the BIOS to find timing settings that works for both sticks in that pair.
But since you said you have two of these graphics cards, you should have enough good RAM chips between the two for one working card. Since you said the bad chips short the Vdd this also makes it easy to find the bad ones to throw away.
Any memory tests you run on a card with no RAM will obviously all fail because none of the RAM is working if its not even soldered on the board. There is no difference between dead RAM and RAM that is not even there, both will not store data hence why it the test says its bad.
Also its not all about just functional tests that the GPU can do its thing. The power supplies on graphics cards are a big part of it too. Modern cards can take an absurd amount of power so they will have switching power supplies rated for 100 200 300W..etc This is a LOT of power for such a tiny switch mode supply. These do fail too (and its possible that it also killed the RAM by shoving a large voltage spike into it) and the only way to properly test these is to get the card to consume as much power as possible and the best way to do that is running 3D benchmarks that give the card a heavy workout (I use FurMark for this) but that will obviously need working RAM to run.