Most airlines at PVG 2 (even the Chinese ones) have bag drop counters for people who have checked-in online. Some carriers even have self service check-in terminals. I use PVG regularly (but not usually on DL) and would be amazed if there was not a dedicated counter for online check-in passengers.
The airport itself at PVG now accepts home-printed boarding passes - I have used these recently departing T2 on BA to LHR, CA internationally, and on AY to HEL. Security at PVG don't seem remotely concerned about these as long as there is a barcode and it successfully scans.
EDITED TO ADD: UA definitely has dedicated counters. AT PEK they also have EasyCheckin machines (not sure about PVG).