Like every other unit in the game, the supply unit can be upgraded. However, the armor of the unit doesn't appear to increase with level, and, at $25, the cost seems significantly lower than that of other units. So what does upgrading the supply unit do, other than to add a star to the unit?
It changes the ability it produces.
0 star: Repair (every 5 kills)
It's so cheep so you can simply choose which you want. Note that the better abilities require more kills to produce