Much of East Asia is Buddhist which is an axial age religion and thus has trouble being pushed back.
For Buddhism and conversion, it's really important to distinguish between Theravada Buddhism and Mahayana Buddhism.
Theravada Buddhism sees itself as following the original teachings of the Buddha, with a focus on personal enlightenment, maintenance of traditions, etc.
Mahayana Buddhism has a more open canon, and sees itself as the "greater vehicle." It believes in multiple Buddhas, and that the better goal is for all beings to become Buddhas and use their enlightenment for the benefit of all beings. In particular, it accepts the belief of bodhisattvas, which are beings that are enlightened enough that they could achieve personal nirvana but choose to delay that so that they can guide and benefit other beings.
The thing is that Theravada Buddhism only really spread to regions which already accepted a similar conceptual universe (Hinduism, Buddhism) already. Theravada started in Sri Lanka and spread to SE Asia (modern Burma, Thailand, Cambodia and Laos) by converting them from the Mahayana Buddhism (and syncretic Hinduism) which was already there.
Mahayana Buddhism, however, is capable of spreading to much wider regions, and did so- Central Asia, East Asia, SE Asia, and a few other regions. However, Mahayana Buddhism also tends to be much more susceptible to conversion to other religions. Modern Indonesia, Afghanistan, Central Asia, the Maldives and a few other regions were once Mahayana Buddhists but have converted to other religions (mostly Islam or Hinduism (in India) or sometimes Theravada Buddhism). This process has even happened recently, in that South Korea now has more Christians than Mahayana Buddhists (though irreligion is more numerous than both of those together).
Theravada Buddhism, however, has been much more resistant to conversion elsewhere. As far as I recall, every country which was once majority Theravada Buddhist still is. (I may have missed one somewhere, but not many).
So in talking whether Buddhist countries in Asia may become Christian, it may be possible for Mahayana Buddhist countries in some circumstances, but is highly unlikely for Theravada Buddhist countries.