Yes, but what YOU said was "what if there were objects 100 billion light years away that we CAN'T see" (or words to that effect).
The point being that we now have imaging capability to detect objects further away than we currently see them, and they aren't there! Which is exactly what on would expect if our estimates of the age of the Universe are correct.
If there were objects 100 billion light years away that we can't detect, it doesn't mean the Universe has to be 100 billion years old. The inflationary phase of the Big Bang inflates spacetime at superluminal speeds, and objects embedded therein are carried along for the ride (this is not a violation of Special Relativity).
Aren't they measuring the farthest white dwarf they can find to determine the age?
They are looking to find the faintest (and hence coolest) white dwarf, not the most distant one. The age is determined by how much the white dwarf has cooled off. All things being equal, coolest white dwarf is the OLDEST white dwarf, and once you identify it and calculate its age, you establish a lower bound for the age of the Universe.