Its possible to curry a variadic function if there is a way to know when you reached the last argument. For example, in a printf-like function you know the number of inputs once you parse the format string.
This example here is a function that sums a variadic list of non-zero numbers. The zero signals the end of the list.
Its certainly very weird though. I wouldn't recommend doing this in real programs.
Does currying even make sense for variadic functions? I can't imagine what that would look like as an implementation.