Since Invoke-VMScript which uses the GuestOperations it relies on the VMware Tools.
The VMware Tools have some rules/requirements.
When you try to use the GuestOperations without a password you receive VIX error 3033, which is VIX_E_EMPTY_PASSWORD_NOT_ALLOWED_IN_GUEST
Afaik there is no option to disable this check by VMware Tools.
Changing the Local Security Policy on the target station doesn't seem to work either.
Question: I don't know which tool you used to remove the password, but can't you set the password to a known value instead of removing it?