Voted "yes"!
As pointed out by some fellow commanders, we already have mechanisms that imply the possibility of system-wide FTL communications:
1. The Kill Warrant Scanner as described in the flavour text of the module.
2. When "Report Crimes against me" is active on your ship, any crime against you is instantly noticed by ALL law enforcing agencies... and not only system-wide!
So I really don't see the argument of "hard science fiction". The FTL comm dam has already been thoroughly broken, so why keep on riding a dead horse?
A point I can understand up to a certain degree is the complaint of our fellow pirates (ARRRR). I wouldn't want my presence to be publicly announced the second I pull my first (first of many, ARRR nr. 2) trader out of supercruise, either. However, if that is your main concern... I see an opportunity for a nice little device that could be implemented in a future patch, namely a comm jammer of sorts... which would not only prevent your victim from screaming "pirate, pirate, save my poor little greeeedy trader soul", but would also prevent the transmission of your crimes (IF you manage to keep your "client's" comms jammed). Everybody wins, right?
Haggis McMoose,
Convoy Enthusiast