I voted yes, but perhaps it only kills like 90% of the population in a system, and requires the largest hull and a HUGE amount of cash to create. also, it might take a few turns before it blows, kinda like a timer, so people would have a chance to fight back. This would also make it a costly venture for the bomb makers as it would take years and an armada of ships (which would be destroyed aswell). People would be hesitant to use it, but there are times when it could be more then handy. For example
You've stumbled onto their breadbasket system, lots of rich productive worlds. Destroying the system would leave them severely crippled. On the other hand, it would tap a huge amount of resources to accomplish. and even then they have a chance to fight back.
Which in my mind is pretty balanced. because well, if it got destroyed (the bomb, before it blows) it would do nothing, but if it detonates, good by system.
However, if this nova bomb is in, perhaps star and planetary generation technologies should be in as well, so you can "rebuild" that perfect system after the damned Tjari collected on your loan and blew it to bits. (after of course, they evacuated their asteroid base orbiting the same system)
Anywho thats just my idea.
EDIT: About the Relations effect of it, i think it should be frowned upon by people who are allied with the receiving end. I mean, if everyone is mortal enemies with the bombed system, why would they get ticked at you for removing the system from the picture?
EDIT2: Its like "You blew up my mortal enemy! how dare you! I now like you less then before!"