VMware knowledge base article Generating a Windows core dump from an ESX virtual machine describes how you can generate a Windows Core dump from an ESX host using the vmdumper utility. You can run ESX console commands from PowerCLI using plink.exe. There are some examples in the VMware PowerCLI Communities. So it must be possible to generate a Windows Core Dump from PowerCLI. I will leave the implementation to you. But I'm always willing to help. 
Regards, Robert