Data centers now account for 4.4% of United States electricity demand, yet the grid-level effectiveness of the renewable energy certificates (RECs) and power purchase agreements (PPAs) hyperscalers use to claim carbon neutrality remains unclear. We develop a game-theoretic model in which a data center operator chooses among RECs, PPAs, and behind-the-meter colocation while generators make entry decisions under endogenous financing costs. The model identifies a timing wedge -- the mismatch between consumption and credited renewable generation -- as a central mechanism through which AI demand degrades reliability, raises prices, and increases emissions even when RECs cover 100% of annual consumption. Colocation with storage addresses this wedge directly and induces the greatest renewable entry by eliminating generator revenue risk. We test these predictions by exploiting the staggered release of large language models as a natural experiment, using difference-in-differences on a novel dataset linking AI activity to local grid outcomes. AI demand significantly increases fossil generation, wholesale prices (up to 25% in treated PJM zones), and outage frequency (0.5--1 additional outages per year) near data centers, with impacts scaling in model size. Data centers with on-site generation exhibit a sign reversal in power-quality effects, consistent with the model's prediction that behind-the-meter capacity absorbs demand spikes. Counterfactual analyses show that edge inference, spatial reallocation, and colocated storage each substantially mitigate grid impacts, while REC-only strategies do not. Together, our results demonstrate that the externalities of AI to the grid are tightly coupled to procurement design and the spatial organization of data center infrastructure.