Dear Jon,
Hi - I personally run both before I do any pre-processing at all. I think the majority of the things I test for (FWHM, eccentricity, median value) are largely independent of calibration (the exact value of too high a median value will change, but since this is mainly to take out frames to close to dawn or near the moon, this isn't a big deal).
I will then take a quick look using Blink at the remaining subs to make sure there are no real problems with the remaining subs (I often remove subs with satellite trails etc since I generally have sufficient data to be choosy, but this is less problematic with large scale removal).
Doing it this way typically removes something like 30% of my subs, giving less work to do in preprocessing (I image remotely and frequently have 30 plus hours of data on an object).
Hope this helps,
Colin