hehe yes, eggs are one of my favourite additions in any sandwich..oh heck, for any carb or protein dish too ;)
The fish sauce lands an interesting flavour dimension to the pickled carrots. I know it may be kinda strange-sounding, esp to those who aren't accustomed to Asian sauces..However, without it, the pickles are not as yummy, in my opinion.
You could try without of course! Or with light soya sauce instead, if that sounds more palatable. =P