Of course they will.
It's not a matter of choice, it will just happen.
People will need to work with the Chinese and bit by bit people will find it expedient to learn Mandarin. Business - manufacturing, services, tourism, etc. - all will benefit from the advantages of better communication. China will increasingly produce a ton of media - films, TV, games, music, and people will learn Mandarin to better access and understand it. They will want to visit China themselves, and tend to learn basic Mandarin to help them get around. They'll meet Chinese people more and more with cultural exchanges and school trips and stuff, and learn Mandarin for fun. Let the decades roll by and eventually half the country will speak at least functional Mandarin.
That's what economic and cultural dominance does.
In 1800, the English elites learnt French. Such was the legacy of France's economic and cultural power in the preceding generations. Then the British and later Americans became dominant, and now the French elites learn English. It's not like the English and French like each other, but they sure as hell learnt each other's language when it was beneficial.