The prompt emission of gamma-ray bursts (GRBs) is widely thought to be radiation from accelerated electrons, but an appreciably larger amount of energy could be carried by accelerated protons, particularly if GRBs are the sources of ultra-high-energy cosmic rays (UHECRs). We model the expected photon spectra for such "proton-dominated" GRBs in the internal shock scenario through Monte Carlo simulations, accounting for various processes related to high-energy electrons and protons. Besides proton and muon synchrotron components, emission from photomeson-induced secondary pair cascades becomes crucial, generally enhancing the GeV-TeV and/or eV-keV photons and offering a signature of UHE protons. In some cases, it can overwhelm the primary electron component and result in GRBs peaking in the 10 MeV-1 GeV range, which may be relevant to some bursts discussed in a recent re-analysis of EGRET TASC data. The dependence of the spectra on key quantities such as the bulk Lorentz factor, magnetic field, and proton-to-electron ratio is nontrivial due to the nonlinear nature of cascading and the interplay of electron- and proton-induced components. Observations by Fermi, ground-based telescopes, and other facilities should test these expectations and provide critical constraints on the proton acceleration efficiency.