OK ***** Dump Question/Statement Time *****
Would it be practical to actualy take moon/star shots but not use them until later into the flight?
Shots are used 'when taken'; they are charted *and* useful later - in the sense of that the earlier fix provides a position from whence one has come. In that sense they are useful *later*.
But that usefulness is very limited -
The pilot would have proceeded by dead reckoning after the last fix. That includes the pilot factoring into her heading drift correction, etc. Typically the flight would have proceeded by DR until the next fix. The idea is then to get a new fix when able; a new fix is needed to validate one's then-present position. DR alone cannot account for undetected changes in wind, etc. along the way since the last fix.
If one cannot get a new fix later in the flight, then one is stuck at the mercies of DR and it's potential errors, i.e. winds having changed along the way since the last fix, etc.
There's more to it. Fred also had a drift meter, so when he could see an object below - a ship, marker of some sort, etc. he might have gotten a good idea of what the actual drift was along the way since the last fix. We don't know how much he was able to use it, for sure. Had he been able to use it, the information should have been helpful to the DR exercise by amending drift and speed by having sorted out the winds aloft by drift observations.
We do know that during the night earlier in the flight Earhart reported overcast conditions - not good for getting star fixes. We also know that she later in the night she reported improved conditions, so Fred may well have gotten a fix somewhere in that break.