The NFL says that the draft will go on as scheduled, despite multiple NFL GM's requesting it be postponed.
http://www.nfl.com/news/story/0ap3000001107472/article/no-plans-to-postpone-upcoming-2020-nfl-draft
If the draft were to be postponed, it would probably be for a short time period. With the cancellation of OTA's & Mini-Camps it is a possibility.
I do think that they should change the format, and have it be a 2 day weekend event. There won't be any fanfare. No glitz and glamour, so there is no reason to have it be 3 days long.
They'll still get big ratings, because there is nothing else in sports going on.