Possible, yes. Practical, no.
You can pretty easily extend housing with a double ended housing ferule. You need this or it can't be done.
For actual shift cable or brake I guess (if you're a maniac), you need a couple special things.
First, a miniature Nicopress tool. Pliers or a hammer might work, but probably not in the space you're working in. I have this tool, I use it to repair a specific piece of rock climbing equipment.
Second, you need swages that perfectly the cable. I don't know what size that is but they can be ordered in lots of 50 or so. I do know they're quite a lot smaller than the garage door swages available at the hardware store.
You should probably run 2 or 3 in a row for security. You also have to have this set up on a fairly long run of exposed cable. Probably the downtube. It's also got to be the last thing you attach, since it won't run through housing. Finally, it'll probably scratch your frame, so wrap them or frame with something.
Or you know, order an $8 cable and wait a couple days.