According to my router logs, each computer running 600 instances of iThena and nothing else (about the most that my old 3rd/4th gen i7 laptops can handle comfortably), uses around 8-10 GB of Internet data per day. It adds up pretty quickly if you have a monthly quota, but it doesn't seem to negatively affect anything else that uses the Internet.
Also, I strongly recommend NOT running it on Linux computers.
The Windows client tasks run for about 3-5 minutes and receive 2 credits each, and each client seems to get a "time out" for a while between tasks which is part of why it's more efficient to run a bunch of clients on one machine.
The Linux client tasks used to run for around 30 minutes, and also get 2 credits each, so already not a good choice compared to the Windows clients. Lately they've been taking 30-50 HOURS to run, using data the whole time, and still only getting 2 credits each.