Does Scala have guards?

Yes, it uses the keyword if. From the Case Classes section of A Tour of Scala, near the bottom:

def isIdentityFun(term: Term): Boolean = term match {
  case Fun(x, Var(y)) if x == y => true
  case _ => false
}

(This isn’t mentioned on the Pattern Matching page, maybe because the Tour is such a quick overview.)

In Haskell, otherwise is actually just a variable bound to True. So it doesn’t add any power to the concept of pattern matching. You can get it just by repeating your initial pattern without the guard:

// if this is your guarded match
  case Fun(x, Var(y)) if x == y => true
// and this is your 'otherwise' match
  case Fun(x, Var(y)) if true => false
// you could just write this:
  case Fun(x, Var(y)) => false