The FSC Admin tool will not do what you are seeking. From the client side you can try: http://<server>:4544/Ping to validate that an FSC responds. Or to validate that the client IP is valid for the Subnet/Mask then you can try: http://<server>:4544/mapClientIPtoFSCs?client=10.244.98.110 You might be able to do something in Batch that launches IE to a specific address (like Ping) but that's about it.
I don't know of a direct way to see which FCC's are talking to which FSC's. Another possibility is running 'fccstat -status | find "Assigned"' on each client and then writing it to excel?