A quick glance at 'The Design of High-Efficiency Turbomachinery' on my bookshelf implies the answer is 'No'. Here's the reasoning:
1. I assume the questioner does mean efficiency, rather than total thrust. One can increase the thrust of a jet engine by using an afterburner, for example, but the efficiency goes down. Increasing efficiency means increasing the miles-per-gallon.
2. A gas turbine is a heat engine, so its efficiency is limited by the Carnot limit. This implies that the efficiency will go up if the combustion temperature goes up (assuming the engine doesn't melt first.)
3. The combustion temperature will be greatest when the fuel-air mixture is stoichiometric, that is, when there's exactly enough air present for all the fuel to burn.
4. All existing jet engines run lean, that is, with more air than is needed to burn all the fuel.
5. Therefore, adding more air will move the engine further away from stoichiometric, lower the combustion temperature, and thus lower the efficiency.
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