If the collection facility is a CSS approved lab, or for that matter, a lab with any integrity then any semen that passes QC standards will work equally well in a flush as in an AI situation.
Semen is very important to the success of a flush or an AI breeding, but so is semen handling and storage, thawing, cleanliness, AI technique, uterine environment, heat detection, cow nutrition, management after AI, and on and on.
A flaw in ANY of those variable can lead to a less than desirable result. Semen gets blamed too often I think.