Does the Altera JTAG server support multiple remote users transfering data using the same server at once?

No, the Altera® JTAG server (jtagserver) does support multiple cables and multiple users connected to the same server at the same time but it will only be able to transfer data through one cable at a time. 

If there are multiple users trying to access the same server and transfer data at the same time then only the user who started transfering data first will have access. The user connected second will need to wait until the first user has completed their data transfer before they will have access to the server to transfer data.