The problem with assuming the Human-Reaper had no purpose in regards to the Reapers' return is that Harbinger says something like, "You have accomplished nothing, we will find another way." This implies that the Human-Reaper, or at least the Collectors, were an essential part of Reaper Return Plan B or C or whatever.
Also, to me, it looks like the Reapers wake up after ME2. While some claim they were merely in shadow, they have running lights. In the last shot, when they are backlit by the Milky Way, you can still see their lights. So, if they were merely in shadow in the first shot, their lights should have still been visible. I'll admit I may be wrong. The only way to know for sure would be to ask the developers what actually happened, but the coming out of dormancy is what it looks like to me.
I don't have a problem with the Reapers being able to reach the Milky Way with only a couple months flight, but it begs some questions. Nazara first tried to send the Invasion Signal to the Citadel about a thousand years ago. That was Plan A. When that failed, Nazara indoctrinated the rachni to conquer the Citadel, Plan A2. After that, Nazara tried to indoctrinate some turians to do it, Plan A3. After that, Nazara enlisted Saren and the geth, Plan A4. Next Harbinger had the Collectors build the TerminReaper. Whether the plan was to attack the Citadel again, Plan A5, or something else, Plan B, we don't know, but Harbinger did say it was linked to the Reapers return.
While there are obvious benefits to Plan A, shutting down the relay system, destroying the government, gaining census records, etc, is the drawback of simply flying to the Milky Way so great that they waited a thousand years and tried to attack the Citadel multiple times? If it turns out that this is a Long March or March of the 10,000 situation for the Reapers, I'll understand. If many Reapers died on the Journey due to lack of power or static build up, it will make sense. If the remaining Reapers are low on power and not 100% effective, it will make sense. If they are all fine and ready to reap, it doesn't make as much sense.
I personally would have liked Arrival to have had its story reworked a bit. We have the Alpha Relay. It is the oldest Relay known in the galaxy. It has all these special, unknown properties. We have Object Rho, a mysterious Reaper Artifact of unknown purpose that is steadily building up power. It turns out that Object Rho is a key. When it interacts with the Alpha Relay, it boosts its power so it functions like the Citadel relay. Shepard has unwittingly returned the Reapers to the galaxy.
I'm not saying that is what really happened. Arrival, as it stands now, wouldn't make any sense, but there are weaknesses in the story. While I don't mind Shepard losing, I don't like the way Arrival did it. It was simply a means of taking two days off the clock and "amping things up." Shepard convienently regains conciousness with just enough time. There just happens to be the Mech control station in the Medical Bay. All his equipment just happens to be in the next room. It's just silly. I would say it's all too convienent, except the indoctrinated are trying to stop the asteroid, and the Reapers do show up if you let the clock run down. I would have much rather they reworked the story. Right now the Reapers are only a threat due to their scale and toys. There plans have been fairly easily thwarted. The only reason they've enjoyed any success is because nobody believes in them. For such ancient and intelligent machines, I would like them to clever. I would have loved for them to have tricked Kenson's team and Shepard into unleashing them.
Of course, that's all just my opinion.