Yes, it's quite common for Japanese tourists in China and Chinese tourists in Japan to communicate in this way.

(By the way, note that 漢字 is transcribed as kanji and hànzi [pronounced HAN-zuh] in Mandarin.)

And that Japanese is now the custodian of kanjis after the simplification imposed by the Chinese Cultural Revolution.

Well, Chinese in Taiwan still uses "traditional" -- i.e. pre-simplication -- characters, which can be more complicated than the Japanese versions.

For example, the character for "to read" is:

讀 in traditional characters (used in Taiwan)
読 in Japanese
读 in simplified characters (used in mainland China)

Sometimes the traditional and Japanese are the same.  For example, the character for "Chinese; Han dynasty" (the kan in kanji and the hàn in hanzi) is:

漢 in traditional or Japanese
汉 in simplified

And sometimes the Japanese and the simplified are the same, but the traditional remains more complex.  For example, the character for "country" is:

國 in traditional
国 in Japanese or simplified

Having studied Japanese before Chinese (using simplified characters), I initially found the simplified version of the characters an appalling abuse upon the language.  But becoming more familiar with them, I realize more and more just how well the simplification was conceived from a pedagogical point of view (facilitating learning based on superficial commonalities or similarities in character components and pronunciations) and appreciate how this must have helped significantly in accelerating the literatization of the gigantic Chinese population.  For all of Mao's abominations, this is one thing I think he can be praised for (another being the bringing up of women's status in Chinese society).

Still, it is a pity that the richness and complexity of traditional Chinese characters had to be sacrificed for the pressing, practical concerns of rapidly educating the population.  I dream that some day China may revert back to traditional characters, both officially and in practice, maybe as part of a campaign to restore different aspects of traditional Chinese culture in general.  This may not be as crazy as it sounds on the face of it, as most Chinese can read traditional characters easily enough anyway, and often are used to doing so from watching TV shows, movies, and karaoke videos with subtitles added in Taiwan.

Truth unfolds in time through a communal process.