An interesting question.
Shimano's 9-speed brifters were listed as double or triple capable. I owned a 9-speed equipped Ultegra equipped tandem and road bike that used identical shifters. The shifters actually had 4 shift positions. On the double I got two shift positions for each chainring. On the triple, the middle ring had two shift positions and the other two rings had one each. I also had flight Deck computers on both bikes that always indicated the right chainring so I'm sure that's the way Shimano intended for them to be set up.
Now the question: What's different about shifters that are either double or triple specific? If it was my bike I'd try to set up the double crankset with the shifters that I have and see if I could make it work to my satisfaction. If it does - great. You just saved $500.00. If it doesn't - oh well - but at least you've learned another lesson in the sometimes mysterious world of bike mechanics. It's the kind of thing that I'd willingly do on a personal bike but I wouldn't try on a customer bike.