OIC. Yes, but you would than have to insulate it with some electrical tape or crimp on a dead end terminal or if you happen to have an insulated female spade terminal, that might be good enough.
You can open the back. I've done it on mine a few times this winter. I see that you have already removed the nut. That is the first step. The trick is to be brave. At the moment the back is about to come off or on, it feel like it's going to break. It hasn't for me, but I was very patient. (I don't know how brittle yours is compared to mine so I can't be held responsible it it breaks. It helps to have a jewelry screw driver or something similarly small to pry it open. All you have to do is get one of those black ridges out of it's slot and the whole back comes off. To close it, I've used either a jewelery screwdriver or a dull razer blade to slip the backing back into the slot. Hold something similarly flat up to the slit and push down on the backing until it's at the same level of the slit. The backing will bow in the middle. Remove the flat razer blade or screwdriver and hope the backing springs back into the slot. I think I had to try it a few time to get the knack of it. Now I know how to do it I could have it on and off in about two minutes.
What did you decide to do with your brown wire. If you leave it in don't forget to protect the other side of the pink wire with insulation described above or better.