How fast could AlphaGo mine bitcoins?
As you said, AlphaGo is "just" a collection of CPU's and GPU's. CPU's can mine at a few dozen megahashes (millions of hashes) per second. GPU's can mine at several dozen gigahashes (billions of hashes) per second. ASIC miners mine at several terahashes (trillions of hashes) per second. So a miner is a 100 to a 1000 times better/faster than a GPU which is a 100 or a 1000 times better/faster than a CPU.

So mining with AlphaGo would be insignificant. You would be better off with even one ASIC miner. If mining with CPU and GPU farms was profitable, people wouldn't bother with ASIC's.