You can spin up cloud infra in claude code by just having it write IaC code. It's very good at this.
I do with it Pulumi, bc you can write some python or typescript for your infrastructure. But there are many infrastructure as code tools to choose from.
Yes, you can and definitely should use Pulumi or other cloud infra for production use cases. The way I envisioned cloudrouter was to give coding agents throwaway VMs, use it to close the loop on its task, and then stop/delete it afterwards...