Just before posting the question, I found this article and became intrigued.
Jakarta: Indonesia's Constitutional Court has no power to alter the death sentences of Bali nine organisers Myuran Sukumaran and Andrew Chan or make any ruling on their case, says Indonesian law expert Tim Lindsey.
Instead, lawyers for the two men hope Indonesian President Joko Widodo will come under political pressure to reassess their pleas for mercy if the court rules that the constitution requires the president to properly consider clemency submissions.
In other words, the only person who could make a difference was Widodo1. The only thing the lawyers could have gained would have been a delay in the executions, prompting time for further pleas to the president.
This article makes things clearer: The case could have had an impact because it challenged the clemency procedures of the president, specifically in regard to foreigners, but the court could not have overturned the death sentences. Normally, its rulings are binding, but this was not so in this case.
1I don't mean to imply that this was all his fault; I apologize if it seems that I do.