Roadies have been riding SS or, more usually, fixed for winter training since God was a boy. The idea is that you have to mash up hills and spin down them, the former for strength/power, the latter for suppleness/cadence. I have a 42/16 FG that I do some interval training on, because there's a two-mile loop round my neighbourhood that includes a couple of modest hills, which are nothing on my road bike but sufficiently challenging on the fixie. Half a dozen laps on the fixie gives me an interval session, keeps me in practice spinning at >150 rpm, and offers a simple way of checking on my fitness by recording my HR and times. (I'm too mean to invest in a power meter)

Riding SS rather than fixed rather diminishes the perceived benefits, because you can coast rather than having to learn to spin at high revs. So you'll get nothing from doing so that you wouldn't get from just sticking your geared bike into the 39/14 and leaving it there for the duration. Having said that, if you like riding the Allez better, ride it. And if it is a nicer ride than your "real" bike, think about maybe putting the gears back on? It isn't compulsory to ride carbon or aluminium...