carpediemracing 

Yes and no.

The power required to turn the wheel over at a particular speed at a particular resistance is independent of cadence. Meaning on a trainer you should use mph only for power comparison. The amount of work required to go, say, 21 mph, is the same whether you're pushing a gear or spinning a gear. The work done is the same.

Your legs will fatigue a bit quicker (but your heart rate won't climb as quickly initially) but the net results are typically the same. In other words if you do a big gear effort or a low gear effort for 10 minutes you'll end up at a similar heart rate. It takes me longer for my heart rate to climb using a big gear but in the end it all washes out. If I start with smaller gears (loading my aerobic system) then as I fatigue I can revert to stressing the muscles more. Or I can start using the muscle side more but I'm overall more fatigued when my heart rate catches up. This is why racers tend to spin most of the time and might use bigger gears for shorter attacks and such.

To illustrate in a different way - Right after I got my power meter I was experimenting to see if I could use different pedaling speeds to climb a particular hill faster. For me it's a 6:30-8:00 effort, it's really steep, and the second half I'm always just trying to keep going, there's no thought of "I need to accelerate". Therefore the bottom of the hill is where I thought I could make the difference.

I tried using bigger gears, smaller gears, longer and shorter cranks, and the end results were close enough that I couldn't factor out one particular variable that was more important than another.

Mind you, this is on a multiple minute hill.

On a 30 second hill then there are some ways to utilize leverage or spinning, depending on what you do well. I'm more a leverage person with high peak power but not much endurance. On such 30 second hills I'm much better in a big gear, roll it over the hill, and I'm good. Other riders are better sitting and spinning. There's one hill in particular that I use as a benchmark as I raced it 5-7 weeks a year for 22? years, typically doing 30-50 laps a week with about 3-4 years where I was doing closer to 80 laps a week. On that hill, for me, I found that using longer cranks and bigger gears really made a difference, even as I got out of shape and heavier. When I'm super fit I can sit and spin but since I have a relatively weak aerobic system and a relatively strong muscular system, it's better for me to load my muscles for short, intense efforts.

However…

There's the whole aspect of training to consider. Cycling isn't like motorsports, where an engine is typically optimized for a particular rpm range. In cycling you train your engine (i.e. your legs) and although there's a coarse "optimal range" (80-100 rpm I think, biomechanically), you can really improve your cycling ability diversity by training at different cadences. For many years, and even now, I'll do low rpm big gear work, like 40-60 rpm in massive gears (53x12, 53x11). I focus on different aspects of the pedal stroke since I can actually think/coordinate my muscles at very low rpms. I also do higher cadence work, typically when my pedal stroke has disintegrated, trying to average 120 rpm for an hour, or doing peak rpm sprints (with virtually zero load). These drills help me smooth out my pedal stroke partially because I'm focusing on smoothing out my pedal stroke. In races I've sprinted at cadences from 70 to 130 rpm, I generally hold 95-110 rpm when sitting in, and, depending on the situation, I'll make efforts at 80-120+ rpm. This is on the road, of course, so with gearing and such. On the track (I've only raced one full season on track) I found myself really limited at the top end and had to make up for my lack of leg speed by using bigger gears. Other riders were much, much, much better than me with pedaling speed and technique.