Although only 22 millisecond pulsars (MSPs) are currently known to exist in the globular cluster (GC) 47 Tucanae, this cluster may harbor 30-60 MSPs, or even up to similar to 200. In this Letter, we model the pulsed curvature radiation (CR) gamma-ray flux expected from a population of MSPs in 47 Tucanae. These MSPs produce gamma rays in their magnetospheres via accelerated electron primaries which are moving along curved magnetic field lines. A GC such as 47 Tucanae containing a large number of MSPs provides the opportunity to study a randomized set of pulsar geometries. Geometry-averaged spectra make the testing of the underlying pulsar model more reliable, since in this case the relative flux uncertainty is reduced by 1 order of magnitude relative to the variation expected for individual pulsars (if the number of visible pulsars N = 100). Our predicted spectra violate the EGRET upper limit at 1 GeV, constraining the product of the number of visible pulsars N and the average integral flux above 1 GeV per pulsar. GLAST LAT should place even more stringent constraints on this product, and may also limit the maximum average accelerating potential by probing the CR spectral tail. For N = 22-200, a GLAST LAT nondetection will lead to the constraints that the average integral flux per pulsar should be lower by factors of 0.03-0.003 than current model predictions.