The pitch starts to settle down the moment your pick leaves the string. If you really never play anything slower than sixteenth notes, maybe that doesn’t matter so much. But if you play eighth notes — and pretty much everyone who bends a string plays eighth, quarter and half notes — it matters a lot. Having your notes decay flat can sound pretty rough.
Best bet: tune to the decayed pitch, and develop your picking technique to minimize how sharp you pull your strings. Trying to tune to one brief moment in a falling trajectory will leave you out of tune most of the time. And picking hard on fast runs will slow you down.