Is it possible to have the Eagle autorouter swap gates or pins on parts allowing such exchanges to untangle traces ?
Indeed this is possible.
If you have groups of pins (e.g. on I/O pins on a uC, or the inputs of a logic gate) that are able to be swapped, then what you do is edit your library component to tell the schematic symbol which pins can be swapped with which.
In the library editor, open your symbol. If you go to the properties of any of the pins in that symbol, you will see a setting called 'Swap Level'. A non-zero value means that any pin with that value can be swapped with another pin with the same non-zero value. E.g. an AND gate with two inputs could have both inputs set to have a swap-level of 1, allowing both to be switched. If you have multiple groups of pins, just set each group to a different swap level.
Once you have set your swap levels, saved, and updated the library in your schematic. You can then swap the pins as you please. You will see a button which shows an AND gate with an arrow pointing to both inputs, which when you hover over it is titled 'Pinswap'. Alternatively you can type pinswap into the command bar to enable the tool. Simply click on the first pin you want to swap, and then the second. If both pins you select have the same swap level, the two connections will be reversed for you in the schematic.
Once you have swapped the pins, you may find you have to tidy up the schematic/layout as the wires/traces directly connected to the pins will be moved so they connect to the new pin.
Somehow I misread your question. I don't think the autorouter has the capability to change your design - TBH it would be quite a dangerous feature if for example you have a symbol with pinswap enabled but you didn't want those pins swapping.
I think the best way to achieve what you want is to try autorouting then look at the results, if you see that the routing would be simpler with pins swapped then rip up the traces around the affected pins, manually swap the pins and then either run the autorouter again to finish things off or route those traces manually.