I've seen a couple videos on youtube that indicate it's not possible. I've used AGOL to edit ine and polygon geometry, primarily in collector. However, I've never tried to move a point's location in AGOL. After uploaded a point file into a Group project in AGOL I noticed a few points were slightly mislocated, probably due to GPS error in the field. When I click on the point I can edit it's attributes, but I'm unable to move the point.
Cheers!
-Adam