I did RAGBRAI last year and rode out to the start from Des Moines. We did RAGBRAI+: 100+ miles every day for 10 days, 1082 total for the 10 days. I did it on a geared bike but saw a few fixed gear riders, not sure they did the whole week though. The only things that would make it tough doing it fixed would be it's hillier at the start and finish (near the rivers) and if you had a few tough headwind days.