Every possible assumption that could lead to a notion of some kind of marginal gain from this could only work under the premise of "all else being equal", which is definitely never, never, never ever going to be the case. You're not racing in a vacuum against an atom-for-atom clone of yourself. Any perceived advantage - misplaced as it would be for reasons already mentioned - would be entirely within your head. (That is, perhaps, until someone came along and ruined it for you by asking something like whether or not the marginal gains of fractions of gear inches you added are offset by the fact that to attain them you have to run those tires at a higher tire pressure than what's ideal to maintain a stable contact patch-to-width ratio - which itself is obvious bullshit since stability differences on such a small scale are almost certainly well within the bounds of any rider's bike handling skill. But just pretend no one would ask that and lead you to do something crazy like get your head all wrapped around ridiculously immaterial marginal gains.)
Why not - I don't know - not make this an uber-complicated games of nanometers and instead focus on simplicity? I know that this is going to be kind of blasphemy for the entire religion that worships at the altar of singlespeed gear ratios, but you know in the end they ... kinda ... don't ... really ... matter, right? At least not in the way people seem to think they do. Racing a bike - any bike, SS or geared - is about "work" - in the physics sense of the term. Everyone racing, whether it's W101 or Mohican or Fair Hill or your weekly local world championships, is racing the same course. That means that in the sense of "work", the displacement component is the same for everyone. If you want to lower your workload in a race, there is only one way to do it - lower the mass you're displacing around the course. Two identical riders - same total mass between bike and rider - will always do exactly the same work on a given course. The winner is just the one who does it faster. And that's much more a function of fitness and (in the case of longer efforts) enough time in the saddle to remain comfortable and in control over time so you don't waste time stopping to rest. What conclusive proof has anyone ever presented to show that faster is an objective function of some gear ratio? For every example I pick of someone ripping it up on a 32:20, I can point to someone else beating the field on a 2:1 or greater. My point is not that there isn't some value in choosing a specific gear ratio - it's just that the choice is going to be more about you than any objective advantage of the gear itself. Stop overthinking bullshit and just get yourself as fit as you can with the time you have to train and then ride the equipment and gear you prefer.