The Short answer is yes, but you will still need to have an IS Policy for the child company and correctly reference upwards. The language is crucial to cover the subsidiary. The parent ISO certification does not transfer to the child as the SOA (Scope) is different and the companies are separate entities.
The way around the issue is to have a Vendor Compliance Policy and apply it to the Parent who is supply a service.
For example; In Australia, NSW eHealth supply services to the Local Health Districts (LHDs). The LHDs reference eHealth policies and procedures in their IS Policy as part of their framework. The eHealth policies explicitly state that their policies and procedures apply to the LHDs when using their services. So the Parent company may need to make some accommodating wording changes to get you across the line. You will still need an Information Security Policy, this is not negotiable.