Piggy-backing on others' recognized lineages?

I am pretty certain that they (the ministry of justice) would not do that. Typically you need to prove, with documents, that you are related to a luxembourg ancestor to order to get civil documents such as birth/marriage/death certificates. So just to call them up on the phone with no way of proving who you are, it is highly unlikely they would give you information about any luxembourg citizen much less any current people that it may have on record.
Now if you went to Luxembourg and at the Bierger Center you could at least physically prove who you are, and they might be willing to tell you if there are any other persons that might have applied under your ancestor but i'm not even sure that would be information they would have.

To me your best bet is to do some genalogy to know who are the decendants of your ancestor are, and then contact them to know if any have done the application, however i can tell you after doing some of my own genealogy in the last few years;
1) its much harder to find relatives that have lived in the last 100 years than older than 100 years (lots of places have privicy laws for births in the last 100 years - like luxembourg)
2) you will be spending a lot more time doing a family tree than just collecting your direct ancestor's documents.

I find it suprising that so many people seem concerned about the price of a few certificates, the price seems fairly insignificant in comparison to the price of the trip to Luxembourg (from North America) in order to submit the phase 2 documents. My $0.02.