Yes. Go 19x19 would be completely intractable on a single machine (one comment is citing a $25 million cost estimate in computing power to train AlphaGo Zero). A more reasonable target would be Go 9x9 but even this would be an extreme challenge on a single machine.
There is an Oracle blog article series about training a close-to-perfect Connect Four player using AlphaZero. Even here, they had to rely on multiple GPUs.
You have to keep in mind that AlphaZero is an extremely sample-inefficient learning technique, even for simple problems. Rather, the strengths of this algorithm is that 1) it is pretty generic and 2) it can leverage huge amounts of computation.
There is an Oracle blog article series about training a close-to-perfect Connect Four player using AlphaZero. Even here, they had to rely on multiple GPUs.
You have to keep in mind that AlphaZero is an extremely sample-inefficient learning technique, even for simple problems. Rather, the strengths of this algorithm is that 1) it is pretty generic and 2) it can leverage huge amounts of computation.