I've tried creating a couple of Berserkers - one single-class, the other using the Berserker / Shapeshifter - and they don't seem to get any of their immunities from using Enrage. I'm not sure what's missing, exactly, but I can definitely confirm a berserker of any level is not immune to fear, and I'm not seeing any portrait icons indicating any effects occurring when I use the ability.
I originally confirmed this by getting Horror cast on me in BG1EE, but I'm not seeing any indications in BG2EE and across multiple installs of TOF that this was a one-time exception.