In the first Back to the Future movie there is a famous exchange where Brown, not believing that Marty McFly is from the future, asks him who is president of the United States in 1985. Marty McFly answers correctly that Ronald Reagan is president, and the Doc is incredulous, calling Reagan "the actor." Now it is certainly true that Ronald Reagan was an actor prior to his political career, but my impression is that he was not exactly an A-list celebrity. The only movie of his that I've seen is Knute Rockne, All American, and it doesn't seem to be one that is well known. So I wonder if a typical American (keep in mind that Brown is a scientist and probably has only a cursory interest in movies) in 1955 would even have been aware of him, because it seems to me that the joke only works if we have the benefit of hindsight. Like, maybe if Back to the Future took place in 2015 McFly might travel back to 1985 and inform an incredulous Doc Brown that Barack Obama "the community organizer" is president, but of course Obama was unknown in 1985 and his past life as a community organizer only became common knowledge because he is now president.
Yes, it's plausible. It's true that Reagan was mostly known as a B-movie actor and mostly had supporting roles in his film career, which was nearly two decades long by 1955. It's also true that Reagan hadn't had the level of career success or financial stability he had hoped for by the early 1950s.
However, in 1954 Reagan was chosen as the host of General Electric Theater, a TV program that was reasonably widely watched and increased Reagan's visibility. His role as a GE pitchman was ramping up just at the moment the film takes place -- Reagan moved his family into a fascinating GE model home the following year (1956). The house was intended to demonstrate everything GE could do for the modern family, and Reagan's family was on display to show it.
The limiting factor that occurs to me is that we don't know how much television Doc watched. But if you look closely, a Reagan movie is playing in the Hill Valley movie theater the week Marty goes back to 1955, so it's not unreasonable to think Doc would be aware of him. Incidentally, Reagan himself loved this joke, and used the phrase "back to the future" in one of his state of the union speeches as a result.
Reagan was fairly well-known in 1955. Yes he wasn't a top actor, but he'd been in some prominent films, like King's Row, and had been married to Best Actress Oscar winner Jane Wyman. If you look at original posters for films he was in, he gets billing--not top billing, but his name is still prominent. He had supporting roles in some major, extremely popular movies, like Dark Victory. Watch the Dark Victory trailer on You Tube-he has 4th billing. And then he got top billing in lesser films that were still very popular, like Bedtime for Bonzo. Think of his as like Rick Moranis--a supporting actor in Ghostbusters, a very popular film, and a lead role in a popular but not hugely well-remembered film like Honey, I Shrunk the Kids.