Yes, and No. Yes, the barrel is inclined at an upward angle, (Launch Angle) in relation to your sight plane. This allows the bullet to travel in an arc through the 1st sight plane (the distance between the barrel exit point and your sights) and then fall back into the 2nd intersection of your sight plane. That would be the range that the rifle is Zeroed in on, whatever range that may be.
No, the bullet never really rises once it leaves the barrel, per say. It's pointed up and only travels in the direction it's pointed. If the barrel were held at absolute level, the bullet would immediately begin to drop the instant it left the barrel. Gravity, Physics.
Drop a ping pong ball off of X height and launch another one straight out, from the same height, regardless of speed, and they will both hit terra firma at the same time.
Does that help?