Migrating transformer inference to the edge requires sustainability considerations that encompass both operation and manufacturing, rather than operational energy alone. Silicon photonics enables high-bandwidth, low-energy matrix multiplication; however, existing microring-resonator-based Dot Product Unit (DPU) organizations have been tailored to convolutional computations and evaluated using analog signaling without accounting for embodied carbon footprints. We adapt three DPU organizations (AMW, MAW, and MWA) to transformer inference workloads and extend each organization to stochastic signaling, yielding six organizations in total. We then calculate their embodied and operational carbon per inference. Across five transformer models and four foundry grids, the photonic system achieves improvements of four, four, and six orders of magnitude in Energy-Delay, Carbon-Delay, and Carbon-Energy Product, respectively, relative to CPUs, while also being compared against H100 SXM5 GPU and TPU v5p baseline systems. Analog-to-stochastic conversion increases die area by 4.3-4.6x and embodied carbon by 4.4-4.8x, while reducing operational energy by approximately 91% and causing embodied carbon to equal or exceed operational carbon per inference. Importantly, the DPU organization and signaling scheme, rather than the foundry grid, are the key determinants of carbon impact. Consequently, the fastest organization (MWA) is not necessarily the most carbon-efficient, whereas MAW-Stochastic offers a favorable balance between sustainability and performance.