If you attempt to synthesize the Generator, you risk breaking your weapon, unless you refine the Generator as less breakable. Unfortunately, there are not any factors to make the Generator immune to breaking. So don't synthesize the Generator....
Oh wait, I wonder if any workshop allows synthesizing the Generator into the weapon... Perhaps not?
I just fired up my game. It's not a Synthesis option, unfortunately, because I wanted to test it.
What I DID mess with, was put a Badge of Refection on a Steeled Earth and threw Adray into a Convictor fight. At a 30% Break chance, he healed over 30 ticks of Thunder Flare damage with his weapon intact, and then the Convictors realized I had a base level team of Mirage/Adray/dead Sophia and swept them.
Either the factor works differently on a weapon and doesn't activate Break(!!!), it doesn't count as "healing" when the HP is already full(still !!!), or I was simply lucky(improbably things happen, and this is the likeliest answer in the first place). I'm definitely messing with this in the near future. --- Seven. Point. Five.
It could be that the weapon break chance is only checked when you make an attack with a weapon, not when you absorb an attack. --- The only opinion one should care about is one's own. We did. You did. Yes we can. No.