I bypassed my entire green connector this past weekend. It was part of a bigger issue though, and I honestly still haven't gotten it separated to see if it's damaged.
I got the bike at auction with no keys. I ordered replacement ignition, fuel cap and cowl locks on eBay. The ignition I purchased was apparently for a GSXR but happened to also fit an SV1000. I had to hack off the plug and solder it in, but it turns out that the switch works a little different than the SV1000 one.
The red and orange wires are the same, but this switch had a green and black/white wire instead of brown and orange/yellow like the SV.
After installation I got the blinking FI light and a code check showed that it was the immobilizer. Also, my blinkers and taillight weren't working.
So, I ended up doing some custom wiring. I wired the red wire normally. I patched the brown (illumination) wire in with the orange wire so lights would get power with ignition on. I wired the black/white wire in with the orange/yellow wire and added the correct resistor jumped between orange and orange/yellow. I didn't use the green wire from the ignition at all.
While I did all of this I bypassed the greern connector as I was getting intermittent "restartancehrances" on the gauge where it would go blank and then come back up, or it would cut off then I tried to engage the starter. I figured I'd rather bypass than hope it was okay and then get stranded. It wasn't a difficult job at all, but the leads I had to work with on the bike side were short after cutting the connector off.