Hi Christopher,
yes, you can connect any legacy (Non SAP System) system with SAP GTS Server. that much of Flexibility has been provided by SAP. so, you can connect the JD Edwards system with your GTS System. But to connect these two systems you need to interface a middle ware (PI or Java Connect , etc.,) to convert the data of JD Edwards to SAP format.
SAP has provided the Function Modules to for both Master Data and Transactional Data using APIs. with the help of your Basis and Technical Consultants you can achieve this.
Thanks,
Srinivas Yellampalli