I think the total opposite is true. If getting into the ASG has been motivation for Conley, the passing of the ASG removes that particular motivation by virtue of it passing. I think the value of the boosted confidence/happiness outweighs the potential chip on his shoulder since the Jazz are not lacking chips as a team, and I certainly think him playing with more bounce is better than the risk that being left out again might be deflating.
On the topic of the collective chip on the shoulder; I'm more worried that the tsunami of disrespect they're weathering is more an impediment than a boost at a certain point.