No. wont happen. each pcie lane will work to it's maximum bandwidth iespective of what's installed in another slot. Al the "limiting" you are going to see is being limited to x1 bandwidth speeds on your external USB devices.
^ slight error in the above post. " each pcie slot/lane will work to it's maximum bandwidth if the installed device's bandwidth is more than that of the slot's." e.g. pcie 3.0 x16 card will run in 2.0 slot at 2.0 speed, in 3.0 slot @ 3.0 speed but still 3.0 speed in a 4.0 slot(whenever that sees the light of the day i.e)