Went in 2005, 2009, and 2013. In 2005 I carried 5 gal of gas with me from Fairbanks to Deadhorse and return. Dumped it in the tank when I got back to Fairbanks because I didn't want to carry it any more - no need to - plenty of places to fuel.
I do carry two pickup spares and a motorhome spare. Have used the pickup spares on every trip to Alaska but that is because I do a lot of off roading. Never had a problem with pickup tires on the main roads.
The only time I had trouble with the motorhome tires, to and from Alaska, was in 2009 when I threw rubber off one between Anchorage and Seward. Glad I had it. Road Side Service paid to have a service truck come out and change it for me. Don't know how long I would have been out of service, and the cost, without the spare. Also used it one time in 2008 in California.
Now I never leave home without the wife and spare tires.
But back to your question. In my opinion - Carry extra gas if it makes you feel safer and you can put up with the odor, BUT IT IS NOT NECESSARY.