Yes, we would expect that.
Looking at the "junk DNA" in different species, we should be able to create a phylogenic tree that resembles phylogenic trees created on the basis of other measures of genetic similarity on and observed characteristics. These trees might not match up perfectly, that's okay, but they should be very, very similar.
New species from a newer branch should have predictably different levels (given orders of magnitude) of junk DNA if Common Descent is actually in play, correct?
I don't understand this. A "newer" species (one that branched off more recently) would still have most of the junk DNA from the older species. We might not expect it to have less new junk DNA than a species that branched off earlier, because their common ancestor would be accumulating junk DNA between the time both species branched off.
It's possible that junk DNA would accumulate more quickly during periods of rapid mutation/evolution, but I don't know if that's the case.
That presumes that most junk DNA was accumulated prior to the branching off into newer species. Do we know that to be the case, or do species accumulate junk DNA on a more regular basis?