Yup,
The downthrust is because the usual engine thrust line is below the centre of gravity of the aircraft (for high wingers) and the plane will want to pich up as soon as you open the throttle.
Even if it's through the centre line, the secondary effect of throttle is to raise the nose by way of longitudinal stability.
The side thrust is because the propellor loading will want to turn the aircraft. Even in straight and level flight, the propellor causes a twisting of the air that acts on the tail of the aircraft that makes it want to yaw left.
Full-size pilots have to correct for this with a bootful of rudder during take-off along with an application of rudder trim. We can't usually apply rudder trim in flight or sense the yaw during pitching manoeuvres, so the designer makes it easier for us by applying a little side thrust (usually about 3 degrees).