Sounds like this software is a 2-part beast. Everything I've read says that you need to have the Windows tray-icon installed. This suggests to me that PhoenixNet is possibly a Plug-n-Play option that Windows would detect and ask you for the Mobo's CDROM in order to install the the tray-icon driver. It's very likely that this is ALL that the BIOS would be capable of doing -- triggering/forcing Windows to install the tray-icon so that "PhoenixNet" can live on your desktop. After all, the BIOS can't tell what O/S is running, or what Ethernet card you've got installed.
It's very doubtful that this will affect Linux-based machines -- especially since Linux switches to Protected Mode and ignores the BIOS once it gets control of the PC. Even if it shows up in the PnP scan, there'd (probably) be no Linux driver installed behind your back. (The driver would have to be part of the Linux Distribution, after all. )
I'm just speculating at this point.. until I have one that runs on one of my Lab Machines, I probably won't be the one to disable this annoying bit of code. More likely, Phoenix will cave like Intel did when they tried to add a unique Serial-Number into the CPU.