The idea is:
GM: “You fell from the crumbling stone stairs, are you already Injured?”
Player: “Yep.”
GM: “Ok, you fall on your feet, but you sprain your ankle, it will count as a Factor 1 for related tests until you recover.”
Is that possible? I mean, I consider it a cool middle ground between a twist and a condition, specially when the characters are heavily worn out.
Stay cool 
It’s definitely not in the rules. You could give them another condition, like afraid or exhausted… or you could kill them, since they’re already injured, but only if they get to succeed at something dramatic as they die. What you are describing is essentially just the Injured condition but applied twice, which seems to be very not Torchbearer.
The thing is, I already have the control over Factors by using the Evil GM rules, this way I’m only making it clear for the player.
Also: it wouldn’t be a relevant Factor for all tests. Following the example it would only apply on some Dungeoneer tests, Scout, Fleeing conflicts or something related.
Stay cool 
I suppose it’s no worse than losing a piece of equipment. It’s essentially just a proper Twist. Consider it “Inadequate Tools” for running around on. I wouldn’t tie it to recovery, though. That way lies madness. Maybe just until the next Phase. It’s probably best to not even mechanize it, and just say, “You’ve sprained your ankle until the next Phase”, and apply the Evil GM factor as needed.
I’m not a fan, for the reason jovialbard describes. You’re essentially introducing a stealth condition as a twist, which means not only are they getting smacked with a penalty, they don’t even get the positive benefit of succeeding at what they were attempting.
I think you should either give them a real condition or give them a real twist. The factors that you’re introducing with Evil GM Factors should be environmental in nature: Mist makes it hard to see, smoke makes it hard to breathe, the path is slick, the hill is covered in loose scree.