Does Blue Sentinel equipped with Skyfall of Areion cause conquer effects to trigger an additional time?

Yes — but only for Blue Sentinel's own effects at that battlefield.

Skyfall of Areion makes the equipped unit's hold effects also count as conquer effects and vice versa, so Blue Sentinel's "When I hold" ability becomes a conquer effect too. Since Blue Sentinel's passive doubles its hold effects ("Your hold effects for holding here trigger an additional time"), and the ability is simultaneously a hold effect and a conquer effect, the passive doubles it during a conquer — this is the exact mirror of Red Brambleback + Skyfall + Trinity Force scoring 3 points on a conquer (FAQ #9537).

The limit: Skyfall's bridge only applies to the equipped unit's text, and Blue Sentinel's passive only covers hold effects, so an unrelated unit's or a battlefield's plain "When you conquer" ability is not doubled. So a conquer with Blue Sentinel + Skyfall gets its hold/conquer effects twice, not every conquer trigger in play.