(Not to mention that the hydrogen line was only discovered in 1951, as a result of years of hearing it using radio equipment invented half a century prior. Even things as basic as the proton took until 1932 to discover.)

So a period of 25 years to go all the way from "weird fringe theory that fixes some issues we've been grappling with for a long time now" to "got it all figured out". The start of that period aligns very closely with the initial invention of radio. And a variable effect due to the hydrogen line can potentially be observed by anyone operating a radio in the relevant band.

The only way this doesn't work is if the aliens who retrieve the plaque from deep space somehow stabilize in the long term at a point where they've developed rocketry and general space travel but not radio or an understanding of quantum mechanics.

However the above would seem to imply that they don't do radio astronomy, don't have a very good understanding of light (since it's all photons), and don't have high frequency electronic circuits (since designing those requires accounting for RF interference). I guess their understanding of optics is also lacking and their understanding of chemistry is rudimentary and stagnant over the long term.

In other words, aliens permanently stuck at a late 1800s technology level that have nonetheless developed the ability to travel across interstellar distances. And spotted voyager (a very small cold object in deep space). And retrieved it intact.

That's undoubtedly a very cool premise for a scifi story but as far as real life goes I think your time would be better spent worrying that voyager might be eaten by a species of space fairing wale.