no it isnt necessary, and in some applications you wouldnt need an ethernet connection or even have one anyway, like for a device that works in a standalone setup
It does help though if you have some way of connecting the target to a PC so you can get it set up and run apps though, a serial connection or ethernet does make it easier, but it isnt necessary.You can easily get the target to run by itself and boot up and run an app right after the boot process.A net connection of somekind allows you to monitor it while it runs and make changes though, but that can be temporary.
To do what it sounds like your doing, Id run the app in question on a linux PC and get it to work the way you want, then transfer it to the target and have the target run it at the end of the boot process automatically, you can do that by adding a call to the app to the local part of the init scripts. Not sure if bluecat uses BSD or sysV init scripts, but if it uses BSD style you can add commands to the /etc/rc.d/rc.local file and they will be run at the very end of the boot process.SysV init scripts are similar,just located in a different directory, not sure off the top of my head where.
check out
http://www.tldp.org and look up "boot process" or search the howto's on booting, that will give you an idea of what a linux system does at boot up.