Actually, Yes and No.
Optical mouse captures image using the sensor and compares current image with the previous one.
Higher the resolution, the better the mouse will be able to tell the difference, and move more precisely. It also will be able to tell the difference between SLIGHT movement on higher DPI mouse, hence it will register more movements, resulting in more movements of the cursor in an inch.
But ultimately, there is sensitivity that is separate from DPI that multiplies the values calculated by the mouse. So with same sensitivity, higher DPI will move more, but moving more is not the main point of higher DPI. Its the accuracy that the user is looking for.
In some situations, you would like to filter your input, and only translate small portion since humans make unnecessary and inefficient movements. Basically you are artificially inflating error margin. This is done by dropping DPI while keeping same sensitivity, hence the DPI toggle in the gaming mouse for FPS.