With a pin drive prop like yours, it doesn't really matter too much, but it is better to tilt it down. The cooling systems on these are designed to completely drain when tilted down. On motors with thru hub exhaust, you need to tilt it down, as rainwater can collect in the hub, and lower unit, and in the winter, freeze.
That being said, during the season, when my boat is getting used every weekend, I don't bother loosening the straps, or taking it off the motor toter. But, when it gets colder or I don't use it so frequently, it is tilted down, and I might actually cover the rig.