I harvested most of my onions when they fell over for 3 reasons:
1) The foliage was all tangled up and I was concerned about spread of disease in mild wet weather.
2) I had more than enough in what was there to last the year.
3) I knew there wasn't much more growth left in them.
So I harvested more than enough for the year, but my sweet onions, which were still upright, and which do not store as well, (Kelsae and Rouge Longue de Florence) are still in the ground.
I know that's not a definitive answer, but it might perhaps act as guidance?