randonneuring on a fixed is quite possible. i've done a 200 on a fixed and ride with guys who do all manner of rando distances on fixies. the benefit of doing rando rides on a fixed is less possibility of mechanical troubles. because some of those rides leave you out in the sticks at all hours, you don't want to be condending with any of the problems shifting bikes offer. and no, riding a brevet is not like riding a century, or a tour, it is more like rally car racing on a bike. except it's not a race. check out my local clubs website (there are a few members who ride fixed on brevets; besides that there are articles on randonneuring to get you aquainted) or the RUSA website for you americans.