That's always how empires are subjugated. An initial invasion force demonstrating their fighting prowess gets some locals to join them, and with that bigger army they can get other big armies to do the same and so on, and if everything works out, they end up with the by far most powerful army around and conquer everything their logistics can reasonably reach.

That's how China got overrun by steppe nomads twice, for example. The unusual thing about the Spanish conquistadores is mostly how little of an initial force they needed to set off an avalanche. Even Genghis Khan had to slowly work to unify the Mongol tribes before he could switch to rapid expansion.