Energy is only needed for acceleration or course-corrections. Moving at a constant speed in near-vaccum is not energy-intensive. ("Sir Isaac Newton is the deadliest son of a ****** in space!")
And stasis pods would be inside the ship, so they'd be wrapped in any time dilation and would not need to experience a million years of real time passing for them -- there is no "universe's timeflow" (just that of an external observer, which the ship would not actually experience, according to the physics).
(And I'm not saying I'm sure this is how they'll do it. I just think it's a lot more plausible than you're giving it credit for. And for the record, I don't mind indoctrination theory either. I understand why people who feel strongly about player agency hate it, but I don't mind that some people like it. If they can come up with a solution that doesn't disprove it, then I think that would be preferable.)
Well, you'd need occasional bursts of speed since due to the universe only being a near vacuum, there is still stuff we would run into and slightly slow us down since millions of years of that would add up. Plus you'd need to start slowing down at around the half way point which would require a lot of energy as well.
Energy goes at the speed of light, so it would have to slow down the faster you go due to the light barrier, which means you'd actually need more energy than the trip would take.
Is it plausible? Absolutely. It's soft science fiction so anything is plausible. But it runs into problems that the lore has established. As for the various theories, I don't care who believes what. I've always had the position that "All interpretations are equally valid". Not only because it allows more people to enjoy the game, but because Bioware wanted exactly this speculation from fans.
I've enjoyed discuissing this by the way. It's fun to discuss astronomy and astronomical physics. 
Phlease. Ark Theory was the main topic where people were speculatin/betting on galaxy swap as one of the "ingredients" of side stepping the endings. Score 1 for us, IT: still lonely 0.
People have been speculating about traveling to other galaxies since ME1. Ark Theory doesn't have claim over anything that involves going to a different galaxy.