No, the "chest piece with no stats" is actually the token for the
tier 7 chestpiece you can turn it at another
vendor (I know this can be confusing).
So, yes, with your badges (from 10 mans or heroic or the "better badges" from 25mans) you can buy two pieces of your tier 7 gear.
The thing you likely want to buy with your 40 badges is the nice
trinket with 84 crit on it and 1k ap as a proc (with a bit less than 1ppm as it seems).