The reason you might run the screen uphill is to slow the rate of material travel, increasing the amount of time the material stays exposed to the deck, providing better odds of the material falling through. Running the screen uphill also changes the exposure of the particles to the openings themselves. Quite often the choice of running a screen uphill is made in finer screening applications where efficiency can be tough.
You will not do any harm to the screen or the mechanism itself by running it uphill. Just make sure you do not increase your bed depth too much or you will have a negative effect rather than a positive one.