Does rooting wipe the /sdcard?
The Official XDA Discussion for CF Auto-Root (The tool OP linked) includes the following line: 


  Note that if your device had not been unlocked before, this procedure will wipe all your data!


So to answer your question:


Does rooting format the /sdcard/ partition?

No, rooting alone will not format the partition mounted at /sdcard/.
When I root for the first time, or root using a tool, could this happen?

Yes. When using a tool provided by a third party (EG: Not you or Google), then you're following the steps their tool defines.

When you first gain root, one of the steps involves unlocking the bootloader. This is really only necessary once, Unlocking the bootloader will perform a full factory reset, erasing everything.