Yes, Roddick drew his more-than-vertical tossing arm even a bit further back just before launch, then visibly threw it forward timed to the racquet drop and leg extension. The other player who did that, viewable in old films? Don Budge.
I find the opinions of many experienced players puzzling. Why the vertical (or beter) tossing arm? Why some vigor (not mere dropping) of the arm upon launch the active service motion? It fulfills the same purpose as the off-arm in the forehand. Just as good players first use the off-arm hand to sight the ball, its angle of rise from the bounce, then swing it left, then pull the elbow in, so the server does the same in the vertical plane. Sighting the toss helps, but the major effect comes from the "assisted drop, then pull-in," of the tossing arm.
To get the thing if it is new to you, drop the straight arm with a slight and quick bit of boost...and also drop it with a slight angle to the left (for righties. Slight. Continue your launch from ca. trophy in the normal way: Simultaneously drop/throw the tossing arm down still straight, drop the racquet back with a loose arm and shoulder to start its free-swinging loop, vigorously extend the legs. Then, just as the racquet bottoms out, is ready to go under and up....pull the tossing arm in, bent elbow, forearm along the stomach.
The result should be that the momentum transferred from the accelerated straight tossing arm is (upon shortening its lever arm) transferred to the torso, and at a slight angle. This boosts rotation speed of the torso in the horizontal plane, which is a benefit. It also pulls the tossing shoulder forward and down, which is good, because OTBE, that supports hitting shoulder rise.
If a player fails to raise the tossing to (or nearly) vertical, or drops it early, or just lets it flop, or times it wrong, he or she loses most all of the benefits mentioned. The function is directly equivalent to the functions of the off-arm in the topspin forehand.
If you are skeptical of the "boosted rotation" reality, just try the tossing arm sequence in your socks, in your rec room, with or without a racquet. Without the use of legs or core muscles, you'll still find your body, torso, rotates when you pull the tossing elbow in. It is easy to control the timing of this boost, so it is very handy at the moment your racquet bottoms out in an actual serve, and needs encouragement to swing back and up. And as if this were not enough, working in a correct tossing arm action and synchronizing it with the rest, is easy mentally and requires almost no physical effort, because gravity is doing the hard work in the drop.