The Pythagorean theorem first appeared in China by the 1st century BC, compiled as part of a mathematical treatise called the Chou Pi Suan Ching. Liu Hui proved the theorem (3rd century AD) in his commentary on the Chiu Chang Suan Shu (Nine Chapters on the Mathematical Art). The Chou Pi Suan Ching may contain an even earlier proof, but it's debatable whether it qualifies. So the answer is yes. A thousand years ago, Chinese as well as Japanese mathematicians (who had access to Chinese mathematical texts) would have been aware of the Pythagorean theorem.

The question of diffusion (the spread of an idea from another culture) versus independent invention/discovery is more difficult to answer. Diffusion is always possible, but notoriously hard to prove because of the lack of sources by intermediary cultures. There are rare exceptions, such as when an entire word problem is based on one from an earlier source. For example, the bamboo problem in the Chiu Chang Suan Shu (circa 1st century BC) reappears several centuries later in a work by Brahmagupta (circa 7th century AD).

However, the absence of evidence doesn't stop some historians from speculating. The Japanese historian of mathematics Mikami Yoshio (1910) theorized that Pythagoras traveled to Asia and received the theorem from Chinese mathematicians. As far as I'm aware, his theory is not adequately substantiated and few (if any) modern historians share his views. But the idea was provocative enough that a translation of the Chiu Chang Suan Shu by Swetz and Kao (1977) contains a chapter with the title of "Was Pythagoras Chinese? An Examination of Right Triangle Theory in Ancient China." In another example outside of East Asia, Boyer (1968) theorized that the Pythagorean triples that appear in the Indian Sulbasutra ultimately originated from Mesopotamia, where the Pythagorean triples appear hundreds of years earlier.

Speculation aside, the oldest record of Pythagorean triples (but it's understood whether they understood the general case of the theorem) comes from Babylonian clay tablets (see Plimpton 322, circa 1820-1762 BC, currently held by Columbia University), which predates the Egyptians, Chinese, Indians, and Greeks. Did the Chinese or Greeks influence subsequent discoveries? Or was the theorem independently discovered at various times in history? It's impossible to say without speculating. Historians have a basic timeline of the history of the Pythagorean theorem, which I've described, but they are limited to the sources that have survived.

For further reading, my main source is Joseph Dauben's chapter on Chinese mathematics in The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook.