Well, maybe.

If riding up a hill in a high gear puts you up near your anaerobic threshold, then you are more likely to bonk. As one gets closer to the anaerobic threshold, your body will burn more glycogen (carbohydrate) than fat. You have limited supplies of glycogen about 2000-2500 calories. Most people have plenty of fat reserves (essentially unlimited). So at lower heart rates, your body should burn a reasonably high percentage of fat compared to glycogen.

However, if you are climbing the hill at the same speed by running very high rpms as you would going out of the saddle in a lower gear, I don't see the advantage. Your heart rate should be about the same and you should be burning up the same amount of glycogen. If you sit and spin up the hill at a slower rate of speed, that should cause your body to burn more fat and save some glycogen which delays glycogen depletion.