Can "to that effect" be used in the way in which it is used in the following sentence?
While ruling out large-scale intervention in sport due to the absence of a power to that effect, the Commission noted that the EU nevertheless had to ensure the compliance of the initiatives taken by national authorities and sports federations with EU law.
However, you cannot use "due to" [not properly at least] in this manner.
"Due to" always requires a form of the "to be" verb first. It is due to.... Otherwise, use because of (you will notice the "be" is embedded in that word!).