As far as global recognition goes (fame outside China), yes it was because of Disney.

But let's back up and examine the question about when Mulan became famous inside of China.

Unfortunately, the answer is what we normally get for such questions: We don't know.

But we do know that the Ballad of Mulan most likely did not become famous during the era of Northern Wei, when most (modern) scholars suppose it was written. (Imperial scholars had their own ideas about when the Ballad was written, but that's a different question entirely)

Several hundred years pass after the Ballad of Mulan is composed... and nobody so much as writes it down. If it was written down, it wasn't preserved. It definitely wasn't treated as highly important literature.

But during the Tang Dynasty (a few centuries later), we see famous poets (Bai Zhuyin, Wei Yuanfu, Du Mu, etc) writing about Mulan. Their poems were extremely short (most were two lines long, with each line consisting one two phrases). You can read the English translation of such one poem here. I can link the Chinese text of other poems if anyone's interested.

Four Tang dynasty poems about Mulan have survived, making some scholars speculate that there must have been many more that we no longer know about.

Keep in mind that what follows is speculation. During this time, an entire genre known as “Mulan poetry “ emerged. These poems largely consisted of (or, so the speculation goes) poets anthropomorphizing magnolia flowers (the Chinese word for Mulan means "magnolia"). The flower sits on a branch, being as beautiful as a woman. When rays of light pierce the petals like swords, the flower (whose name is Mulan, of course) grabs the swords and dances in the wind.

Note: Many people are skeptical of Mulan poetry and think that the anthropomorphization of the magnolia flower had nothing to do with Mulan.

Keep in mind that the Ballad of Mulan was written first. So, the legend didn't grow out of Mulan poetry and the anthropomorphization of the magnolia flower. Rather, the legend began with a woman taking her father's place, then devolved into cute poems about flowers.

As I said, this is speculation. But it explains why the legend was lost for the next several hundred years: famous poets pretty much stole it and then derailed it. First, the poems were all about a magnolia flower named Mulan. Then, the flower’s name changed to Yulan (another name for magnolia). Soon, the poems weren't even about magnolia, and we’re just poems about random flowers.

Before long, Mulan had been all but forgotten.

In the Ming dynasty, Xu Wei picked up the "original" version of the legend (well, at least his play was about more than just flowers dancing in the sunlight). But as far as we know, his play The Heroine Mulan Goes to War in Her Father's Place (circa 1580) was never performed. I can't seem to find it (I'll link it if I do) but I remember reading a lengthy dissertation theorizing that the play was performed inside of people's houses (as private performances), which is why we never had any record of it. The play itself is rather erotic (Mulan changes costume in front of the audience), which could explain its private nature.

But again, this is more speculation. The one thing we do know is that Mulan wasn't famous yet.

Or was she famous in a different way?

We’re used to thinking about legends develop through literature. But the people could have certainly continued talking about Mulan in their everyday speech. Once again, this is more speculation... but parents could have reminded their children about Mulan. Of course, we have no way of knowing whether this was really the case, but it would explain how the legend stayed alive even when there were long gaps of several centuries between authors writing about Mulan.

During the Qing dynasty, Mulan finally starting becoming a prominent figure in Chinese literature.

China was now under Manchu rule. The Manchu (who were not Han Chinese) abused their power. They tried to force the Chinese people to abandon their Confucian values. They even commanded Li Chengdong and his Chinese soldiers to slaughter any of their own Chinese brethren who refused to shave their heads and wear the Manchu hairstyle (Confucius taught that it was a disgrace to cut one's hair).

During this time, we see three novels about Mulan arise. Romance of Sui and Tang (1695) and The Complete Account of Extraordinary Mulan (circa 1800) were highly politically motivated. I've read them... and I'll just say there's a reason why they never became famous. I had to power through some really boring scenes. And that's saying a lot, as I'm a huge fan of Mulan and Chinese literature.

To give you an example, multiple chapters of The Complete Account of Extraordinary Mulan are devoted to characters just sitting around and talking about calligraphy. The goal is to show the reader that Chinese people are highly cultured so that the reader will understand that non-Chinese people are barbaric by comparison. (Subtle stab at the Manchu here.)

Romance of Sui and Tang is much less subtle. Mulan starts out being devoted to the Tujue, but changes sides when she's captured by a Chinese princess. All the Chinese characters are unbelievably nice (imagine a world where everyone is Mr. Rodgers) and all the non-Chinese characters are pure evil. It's just a purely one-dimesional plot.

The only Qing dynasty novel I actually enjoyed reading was The Fierce and Filial Girl from Northern Wei (circa 1850). The book actually has depth (we have both good and bad Chinese people! And good and bad non-Chinese characters!) but the writing is atrocious. The author doesn't think things through, doesn't tie up plot holes... it's entertaining, but frustrating at the same time.

For instance, the enemy princess helps Mulan escape, but claims that she was visiting her parents so that the enemy king won't suspect her of helping Mulan. But the author seems to have forgotten that the princess is an orphan (oops) and the king is her cousin (so, it's not like the king didn't know). It's a fun book, and I really recommend it (if you know Chinese), but I'm sure that the author didn't think more than a chapter or two ahead as he was writing it.

Fun fact: The final battle scene in his novel involves using cannons to induce a landslide. Guess which movie later incorporated this into its plot?

Although it’s impossible to prove, I really believe that the legend of Mulan really continued living throughout this era in oral tradition. We see so many failed attempts to bring Mulan’s story to life. Why would authors keep trying when every story about her seems to be a flop?

It’s almost as if the authors knew that there was a fantastic story somewhere in there. After all, the idea about a woman taking her father’s place is so wonderful that everyone had to keep trying to wrap a story around this legendary maiden warrior.

Even though nobody had really succeeded in turning the legend of Mulan into a classic, authors just had to keep trying.

Shortly after imperial China fell, the world wars broke out. Wars mean a need for soldiers. And this is when the legend of Mulan finally started getting engaging. No more lengthy scenes where characters just discuss calligraphy.

The 1939 movie Mulan joins the Army actually had English subtitles (I'm assuming for the English speakers in Hong Kong?). The film was quite successful. Incidentally, this is the first retelling that included romance. The subtle message was... join the army and you'll discover your true purpose in life... and your true love!

Because this movie had English subtitles back in 1939, this provided the first opportunity for Mulan's story to go global... but it didn't. The movie was a great success inside of China, but almost nobody in the rest of the world heard about it (being that the world was at war, everyone else was busy pushing for their own nation's icons).

In 1976, Maxine Hong Kingston published her book The Woman Warrior. This really helped Mulan start gaining recognition outside of China. But still, the fame of Kingston's book was nothing compared to what happened next.

In 1998, Disney made their animated movie about Mulan. And it's because of that movie that Mulan really reached legendary status in the non-Chinese speaking world.

Prior to Disney’s Mulan, there were several successful film adaptations of Mulan’s story. But ironically, it wasn’t until the era of film that Mulan finally started having a decent story. The Chinese people had been trying for centuries to wrap a decent story around this amazing legend for centuries, and finally figured out how...

...and then, Disney came in and basically just got lucky. They jumped onto the Mulan ride just as it was taking off. As the film giant of the world, they took the cake.