I'm glad everyone likes the idea. Thank you. 
Makes sense, as the one we entered in ME2 was said to be capable of abducting every human in the Terminus Systems, and even more than that...
Yeah, it had a capacity of carrying millions of people aboard it in stasis pods, with most of its space to spare.
There's no way that this is accurate. The SR2 isn't 1/4 of the size of a Reaper capital ship, that would make the SR2 over 500 meters long. It's actually less than 200 meters long.
That's true. It seems the size comparison made a goof with that. Still, the Collector Cruiser/Black Ark is as large as a Reaper Dreadnought, or at least very close.
The Normandy SR2 I read is about 220 meters long and the Collector Cruiser is about 8.5 times longer, measuring to 1,875 meters long. For a size comparison from another franchise, it is slightly larger than an Imperial-class Star Destroyer from the Star Wars universe.
I actually liked this idea, and it would make a great begging for the game, as you board one of the Collector's Ships in the middle of the reaper war.
But probably this won't happen, because it would require prior knowledge of the other games, or a infodump right at the beginning.
Chances are they'll have the game start when we get to Andromeda or have been there already a little bit, but I can see them including something about it in the opening crawl they have with every Mass Effect game. Something like:
In the year 22nd century, the Milky Way was assaulted by a sentient machine race bent on galactic extinction known as the Reapers. During/After the war, a plan was conceived to ensure the survival of the various races. The Council/Alliance/etc managed to capture one of the Reaper ships, and turned it from a tool of destruction to a tool of salvation. The ARKCON Pathfinder Initiative was founded and its mission to find and establish a new home was launched.
I like the idea. It is about the only one I have heard that fits the lore of the setting without saying poof wormhole. I can see another take on this where this isn't a council plan but a collector abduction with some kind of prison break. I think your core plan is better but they seem to be trying to copy open world things from elder scrolls and that is how like every elder scrolls happen,(released, or escaped) and similar to the beginning of dragon age Inquisition.
Well, Bioware has said our new protagonist won't be an established soldier like Shepard was. Maybe if they go the route you're referring to we start as a civilian that was captured than freed by a boarding party as they took the ship from the Collectors, and later we join the ARKCON Pathfinder Initiative.