Flexible Layout/Autorouting with GPIO Pins (Eagle)
No. The auto-router cannot change which pin is connected where. 

Very few things in the layout editor are allowed to back annotate the schematic. This is a safety feature to prevent the schematic getting modified without you specifically going and doing so. The last thing you want is for the autorouter to start wiring things up differently from the schematic...

The solution is to let it tie itself up in knots, and then once it is done, manually make the required changes to untangle the knots. The autorouter is not a be all to end all. It is a tool to help with the routing, yes, but it is up to you as the designer to clean up after it and ensure the traces go sensible places and are reasonable thicknesses (etc.).



Furthermore, swapping GPIOs is not always straight forward. You might require hardware serial or SPI interfaces. These are typically on fixed pins. How is the autorouter to know that. Maybe in a different design you don't need the SPI and are free to swap those pins around, again how is it to know that. If it is the same library symbol, it couldn't tell between different designs how flexible you are with pins.