Whilst the FPGA is being configured the pins are tri-stated. Any internal pull-up resistors you might have enabled, won't actually be active until configuration is complete. So during configuration unless another device pulls the signals one way or another, the signals connecting your FPGA to other devices will be floating.
Whether or not you need pull ups/downs on those signals depends on how the other devices will behave with floating inputs - if you need to guarantee that their pins are held in a certain state then you will need pull-ups/downs.
There's no simple answer other than looking at the details of your design. As an example though:
Say you have multiple devices hanging off a bus - i.e. different devices can drive the same signals. Each device has an enable signal from the FPGA to prevent this conflict. While the FPGA is configuring itself you will need to pull up/down these enable lines to stop the devices fighting each other and causing damage.
Hope this helps.