Yes, it does run. I did it yesterday, and I uploaded a video of it running SSBM:
AMD X2 4200+, 1 GB RAM, 64-bit Linux (but it's the 32-bit Dolphin). I tried getting the 64-bit Dolphin to work, it compiles but SSBM just instantly crashes, and an older SVN revision is extremely slow (around 0.1 fps

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:linux: