According to our sister site, Space, the Sun will turn into a red giant and envelope the Earth in roughly five billion years. This Game Boy will manage to mine a Bitcoin block in… perhaps a couple of quadrillion years? Let's just say the portable 8-bit console first released in 1989 isn't much of a mining rig, and by the time it nets a successful hash the solar system as we know it will be gone, but you probably guessed that already.
YouTube channel stacksmashing (via TweakTown) gave it a shot nevertheless, and I have to say watching someone turn a childhood favourite into a miniscule mining machine is entertaining to watch despite being doomed from the very beginning—even with gaming's uncomfortable relationship with cryptocurrency mining today.
The key to the Game Boy's mining capability actually lies in the Raspberry Pi Pico, a low-cost and tiny Pi board that can set you back as little as $4. Since the Game Boy has no way to communicate with the Bitcoin network, the Pico will take care of that. A modified Link Cable connects the Game Boy to the Pico (via logic shifter to shift the voltage from 5V to the 3.3V required by the Pico) and the Pico connects to a PC.
Add in a modified Game Boy cartridge with USB flash drive onboard filled with the necessary mining ROMs and away you go.
Bitcoin is almost exclusively mined by ASICs, or Application Specific Integrated Circuits nowadays, not GPUs. These are now available with hash rates upwards of 100TH/s, with the Antminer S19 Pro managing 110TH/s.
The modded Game Boy will manage 0.8H/s off its miniscule Sharp LR35902 CPU. That's hashes per second and not megahashes per second, by the way.
The S19 Pro gobbles up 3,250W, though, so the Game Boy's four AA batteries may make it just a little less power hungry. It's not very efficient, though.
The Game Boy was at least perfectly capable of mining a custom empty Bitcoin blockchain with a very low difficulty. Success!