If I didn't know any japanese, could I potentially communicate with Japanese people just by writing in traditional Chinese? I've heard and seen this in movies, how true is this?
With well-educated young adults, it's likely that you can.
Japanese junior high and high school students learn kanbun (i.e. ancient Chinese poems and literature) at school in a very unique way with some special marks that compensate for the difference in grammar. Those with ambition of going to top colleges would study the subject very hard, so you might be able to communicate with it. But again, it's only for entrance exams so as they get older they might forget it.
Do you mean words or sentences?
For word, they can understand common words exist in both Chinese and Japanese and have the same meaning, of course. But there are still words that exist only in Chinese or Japanese, and words having different (or opposite) meaning in Chinese and Japanese. Like
daughter in Japanese, but
mother in Chinese.
For sentences or passages, no. Classic Chinese is taught in Japanese schools, but it is still hard to understand for general population. Only well educated people (in some special research fields) can understand classic Chinese well. The Chinese language we use today, even written Tradition Chinese scripts, is a lot different from classic Chinese, and maybe only taught in language schools ( I guess ). So it'll be nearly impossible for people who have not learned Chinese to understand.
In short, no.
Even for 漢字 that exist in both languages, not all are semantically equivalent.
勉強. One of its main meaning in Japanese is "study". In Chinese it means "to force/push oneself (reluctantly)".
Also consider the grammar.
的 in Chinese is similar to
の (genitive case marker). In Japanese,
的 produces an adjective from a noun.