Yes, it is possible, not common, but possible. In this case it is a bit unpracticle, counting backwards this way, keeping track of which year is meant. But we have the standard. You could say for instance: "På mormors mormors tid" (during the life of my grandmother's grandmother's). Another very common thing is at Christmas, where we call Christmas Eve = 'Dopparedagen', and counts how many days there are left, e.g.: "Idag är dag dan före dan före dan före dan före dan före dopparedagen" (this we could say on 19th of December).
jaja, if you translate directly. I'm guessing the main challenge with the learning language websites is that they want to teach you something specific, and point out something. While when you actually translate stuff, you don't translate word after word, you translate meaning after meaning. so yeah... I was only friendly suggesting that the other variant should be also included, since it shows that the person actually understands the meaning of the sentence, whilst "the year before last" sounds a bit confusing and calque. But that's just me.
The thing is that there is still a differens, words are never exactly synonymous. Two years ago (för två år sedan) might concern what I did at Christmas two years ago - while The year before last (förrförra året) is more about the whole year 2012, so to become really good translators we have to feel even slight differences like this.
For me, "the year before last" is extremely common. For me, "the year before the last one" sounds odd. But in Google, I see about 500,000 hits for "the year before the last one", so maybe this is a regional thing. (But still, there are over a million hits for "the year before last".)