Was it famous beyond classical music fans anyway? Was it one of the better known pieces of classical music, like say The 1812 Overture or The Barber of Seville?
And similarly, Richard Strauss’ Also Sprach Zarathustra is probably one of the most recognizable pieces ever. But was it Stanley Kubrick who really made it famous?
My grandfather was pleased to see his grandchildren had an interest in classical music when he saw them crowded around the tv. Then someone explained about The Lone Ranger 
When I listened to the whole thing I was surprised that there were other bits used in other entertainment. Like the morning song used in Looney Tunes. That’s been around longer then the Lone Ranger, right?
A few months ago, The Brooklyn Symphony(?) did the William Tell Overture on Letterman. It included the morning song bit and then went to the Lone Ranger part. I recognized the entire thing as having come Looney Tunes in various parts.
Carl Stalling used it often, not only to represent morning, but to represent storms. I got most of my background in classical music from Merrie Melodies. 
Going further back, Rossini was a very popular composer in his day (he’s been likened to a rock star), so the piece was fairly well known.
The piece may have been well known to opera buffs, but I doubt it. Most opera companies never perform “William Tell” (“The Barber of Seville” is the only Rossini opera that’s part of most opera companies repertories). “The Lone Ranger” kept the overture alive, but the opera itself would be pretty much forgotten if not for the masked man.
Did Rossini know that he was writing terrific “chase” music? I can’t listen to it without picturing horses galloping at breakneck speed and leaping over fences and streams. Great stuff!
I believe William Tell did have an adventurous life, so I think that Rossini did know he was writing terrific chase music. The famous ‘apple shooting’ incident was intended, I believe, as a punishment - he had to risk the life of his own son by the skin of his famed skills. There’s a whole tale surrounding that involving prison escapes.
Something like that, anyway.
I would say it was famous before the Lone Ranger, as I remembr my mother singing (definitely the Willl Tell thing) around the house when I was kneehigh to a creepy-crawly thing.
I don’t know for certain, but I’d be willing to bet that it was. Classical music was a lot more popular earlier in this century, and going to a concert or opera wasn’t necessarily a “highbrow” experience. Even if William Tell wasn’t performed as an entire opera, I’ll bet that the overture was played in concert and on the radio.
Pure speculation: for silent movies, a theater pianist or organist would play it to chase scenes. The transition to radio (and from there, to TV) would be natural.