[Kevin Sevcik]

As long as the force vector from the fan is parallel to the ground, or has an upward/lifting component, then it's not increasing the normal force. This is from a simple sum of forces in the vertical direction, and the assumption that the robot center of mass isn't accelerating vertically. F=ma, and all that, so if a = 0, then F=0. If the fan isn't contributing any force in the vertical direction, then there's no NET increase in the normal force.

Now, it's definitely the case that the fan is shifting the balance of the normal forces on the wheels. The force it's applying isn't going to be entirely balanced by other horizontal forces, so the sum of the moments on the robot isn't going to balance out without the front wheels applying more normal force than the back wheels. But this doesn't increase the total normal force, it just changes where it's being divvied up.

You'll have the same shifting of normal forces from your robot simply accelerating forwards using its wheels. This is why the front end of cars pop up and the rear end sinks when you floor the gas from a stop. But the car isn't getting pushed into the ground any more or less than it was before, unless it actually lifts the front wheels off the ground.