Recent concerns surrounding climate change and the contribution of fossil fuels to greenhouse gas (GHG) emissions have sparked interest and advancements in renewable energy sources including wind, solar, and hydroelectricity. These energy sources, often referred to as "clean energy", generate no operational onsite GHG emissions. They also offer the potential for clean hydrogen production through water electrolysis, presenting a viable solution to create an environmentally friendly alternative energy carrier with the potential to decarbonize industrial processes reliant on hydrogen. To conduct a full life cycle analysis, it is crucial to account for the embodied emissions associated with renewable and nuclear power generation plants as they can significantly impact the GHG emissions linked to hydrogen production and its derived products. In this work, we conducted a comprehensive analysis of the embodied emissions associated with solar photovoltaic (PV), wind, hydro, and nuclear electricity. We investigated the implications of including plant-embodied emissions in the overall emission estimates of electrolysis hydrogen production and subsequently on the production of synthetic ammonia, methanol, and Fischer-Tropsch (FT) fuels. Results show that average embodied GHG emissions of solar PV, wind, hydro, and nuclear electricity generation in the United States (U.S.) were estimated to be 37, 9.8, 7.2, and 0.3 g CO2 e/kWh, respectively. Life cycle GHG emissions of electrolytic hydrogen produced from solar PV, wind, and hydroelectricity were estimated as 2.1, 0.6, and 0.4 kg of CO2 e/kg of H2, respectively, in contrast to the zero-emissions often used when the embodied emissions in their construction were excluded. Average life cycle emission estimates (CO2 e/kg) of synthetic ammonia, methanol, and FT-fuel from solar PV electricity are increased by 5.5, 16, and 49 times, respectively, compared to the case when embodied emissions are excluded. This change also depends on the local irradiance for solar power, which can result in a further increase of GHG emissions by 35-41% in areas of low irradiance or reduce GHG emissions by 21-25% in areas with higher irradiance.