AncestryDNA would absolutely give conclusive proof of either close blood relationship or lack thereof. In practice, it’s just as good as a paternity test.

The only caveats I can think of are:

• Both parent and (potential) child would have to get the test.
• I guess if AncestryDNA just completely messed up and represented some random other person’s DNA as the parent’s or child’s, that would give false negatives.
• Chimerism.
• AncestryDNA might not be admissable in court.

And of those, the first three are just as applicable to paternity tests as they are to AncestryDNA.