In default Sitecore installation, this settings is not even used.
Sitecore.Publishing.Pipelines.Publish.OverridePublishContext processor overrides it anyway. It's only when this processor is disabled, the settings is used. But even then, only the publishing server is affected.
From what I know, CD server does not "receive" the published context, it only receives remote events related to publishing.
Just so it's more clear, here is the comment from config file for
This processor overrides the DisableDatabaseCaches and the MaxDegreeOfParallelism properties of the PublishContext class.
The DisableDatabaseCaches property of the PublishContext is overridden and set to true if child items are being published,
including when you perform a full site publish.
If only a single item is being published, the property is set to false.
If you disable this processor, the publish context uses the value of the Publishing.DisableDatabaseCaches setting for all the
If only a single item is being published, the MaxDegreeOfParallelism property of the PublishContext is overridden to 1.
This disables parallel publishing for single item publishing operations.
<processor type="Sitecore.Publishing.Pipelines.Publish.OverridePublishContext, Sitecore.Kernel"/>