Configuration should complete even in the case where you do not have an external pullup resistor for DONE. Changes have been made to the DONE structure for 7 series devices.
An additional software change has also been made. The "DonePipe" option is now turned on by default. This will allow for the insertion of a second register to the DONE signal prior to being read by any logic. The DonePipe change is documented in (Xilinx Answer 44237). If the "DonePipe" option is disabled, then an external pullup needs to be added.
These changes make the DONE transition more robust and not as prone to issues with slow rise time as in previous families. The DONE pin can still be used to drive an LED using an appropriate external resistor value.