Absolutely. Mickey Mouse was a major hit across the United States within the first year after the premiere of Steamboat Willie in November 1928. Walt Disney was not only able to parlay the success of that cartoon into a distribution deal with Columbia Pictures, he was able to parlay it into two cartoon series--the second series being Silly Symphonies. That was a big deal back in the late 1920s, when most cartoon studios only had one series going at a time. He was so popular, he made a cameo in a live action film in 1931 entitled Around the World in 80 Minutes with Douglas Fairbanks.

By 1930, Disney was selling $300,000 worth of merchandise per year. In 1935, they sold $35 million worth of merchandise. Adjusted for inflation, that was about $639 million!

In 1930, the Mickey Mouse Club was started. This wasn't a TV show or even a cartoon per se. A film exhibitor started showing Mickey Mouse and Silly Symphony cartoons back-to-back on Saturday mornings to entice kids into the theater, which proved to be a big success. The Disney Company got word of it, and made it an official fan club, offering their back catalog to theaters to show to kids who would join the club. By joining, you got a newsletter and admission to the theater during Mickey Mouse viewing parties.

Merchandising for Mickey Mouse began as early as the end of 1928. Some early merchandise included the introduction of Mickey Mouse school tablets in 1929, plush dolls by 1930, and toys by 1931. These licensed products would often be produced by various department stores around the country, to entice shoppers into their stores, often using newspaper ads and store displays to get the word out.

There were novelty songs about Mickey Mouse as early as 1930, and while not a Mickey Mouse cartoon, the Silly Symphony "The Three Little Pigs" in 1933, produced a major hit record with "Who's Afraid of the Big Bad Wolf". To that end, Disney's Silly Symphonies were also honored by winning the Oscar for Best Animated Short for the first eight years of the award's history, beginning in 1931-32, and 10 of the first 11 years the award was offered.

According to the July 26, 1931, edition of the Hartford Courant, by mid-1931, there had already been a Mickey Mouse fan convention thrown in Milwaukee, and dance halls around the country had thrown "Mickey Mouse Balls" to attract patrons in their doors.

Elsewhere, in New York City, a Mickey Mouse balloon first debuted at the Macy's Thanksgiving Day Parade in 1934.

So, yes, Mickey Mouse was a big deal pretty much right away. He was so popular that his name was already being used as an adjective by 1936!