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A larger resolution means basically more data to process. So to answer your question, yes it will slow down your algorithm because basically you still need to read in a complete frame and then process a region of interest, which means more data in the first step of acquiring frames.
However, some smart camera's allow you to read in a predefined region of interest of your actual camera CCD/CMOS sensor, but this only helps in specific cases where you know the actual region of processing beforehand.
Also, if your region of interest stays equal, but the amount of pixels inside it rises due to larger resolution, the process time of that region of interest will also go up. Keep this in mind.
Getting real time processing algorithms is always a tradeoff between resolution, fps, processing power, ... it is something you will need to dig into and experience through trial and error.
