No. For any given scenario, you will get the same outcome regardless of the order in which you move the sliders. Each time you make a change in En-ROADS (such as moving a slider), the simulator runs the scenario again. All the changes that you have made start together, except those which have a delay you have specified based on a slider (e.g. carbon price start year).
However, the change that each action makes will appear different depending on the order in which you move the sliders. For example, in this scenario (we'll call it Scenario A), Buildings and Industry Energy Efficiency is increased to 4.5%/year. Notice the temperature change due to this one action. Now add a carbon price of $100/ton CO2, resulting in Scenario B. Compare the temperature outcome to the outcome if you reset the simulator to the default, and add a carbon price of $100/ton CO2: Scenario C. Then increase Buildings and Industry Energy Efficiency to 4.5%/year: Scenario D. You’ll notice that the outcome is the same in both Scenario B and D, but when you change Scenario C into Scenario D, it appears that increasing energy efficiency has a smaller effect on temperature change than when you increased it from Scenario A to Scenario B. This is because the carbon price already caused some energy efficiency gains, as carbon-intensive energy became more expensive and created an incentive for greater energy efficiency.