Hi AK350
The purpose of using a dialog is to hopefully execute the logic within the dialog and try avoiding custom plugins. However you might find dialog is not powerful enough, but you like the UI, so you want to extend by using plugin.
If you want to pass the information from dialog to plugin, I would create additional fields in the contact entity and the dialog then writes the responses, or summary of what the plugin must do (eg. Plugin action: create case, update parent account, etc.). The plugin can then trigger on change of these fields in contact record.
I would attach the plugin to contact entity and not dialog entity.
Hope that makes sense.