We're using JIRA Agile (GreenHopper) - are there any conflicts with Structure? Can we see the Structure's hierarchy in JIRA Agile?
You can use JIRA Agile and Structure side by side. Structure plugin stores its data in a separate place, so it will not conflict with any other plug-in.
By default, Structure's hierarchy and issue order are independent from JIRA Agile's, but you can install a JIRA Agile (GreenHopper) Synchronizer to have Agile Rank synchronized with the position in the Structure and Epics synchronized with the positions of stories under epics in the Structure.
JIRA Agile displays the hierarchy of a selected issue in a separate Structure-provided tab in the issue details panel.