A sort of:
Documenti = Documenti
.OrderBy(o => string.IsNullOrEmpty(o.Note))
.ThenBy(o => Int32.TryParse(o.Note))
.ToList();
C# 7 has some new features that make this even easier
var ints = from a in str.Split(',').Select(s=> new { valid = int.TryParse(s, out int i), result = i })
where a.valid
select a.result;
or as you are asking specifically about sorting
var ints = from a in str.Split(',')
orderby (int.TryParse(s, out int i) ? i : 0 )
select a.result;