That doesn't quite make sense.
It's true that over a full season randomness doesn't have enough impact to propel a team like Stoke or Burnley to a league title, or even CL football. It doesn't have enough impact to get Emirates Marketing Project relegated. But that's not the same as randomness having very little impact, because I really don't think any factor has to be large enough to win Stoke the league (or get CL football) to be considered to have an impact beyond "very little".
As an analogy this is like saying that over a season Sergio Aguero has very little impact, because if he played for Burnely they still wouldn't get regular titles.
Being conservative I think luck/randomness can quite easily have a 5+ point impact on a team over a season. This is clearly enough to have a significant, and meaningful, impact.