Yes. The way the tributary system works is that China demands acknowledgement of China as superior from foreign states before any formal relations can begin. The tributary state will then send tribute to China in return for China to acknowledge that they exist, and then hopefully give much-desired Chinese goods back for their trouble. Often China didn't enforce the issue - after all, if the barbarians of the periphery did not want to bask in the glory of the Middle Kingdom, the only civilized place in the world that mattered (in Chinese eyes), it's entirely their loss. And before the coming of the Europeans, the Chinese assumption was true - lots of states participated in the so-called tributary trade because Chinese goods were in such demand that the literal kowtow to the Chinese wasn't that much of an issue. On the other hand, emissaries of a foreign country could perform all the rituals that China demands, while reporting to their home country that they did not sacrifice their country's dignity - and that's what Japan did most of the time.

At the beginnings of Sino-Japanese relations, Japan accepted China's suzerainty as evidenced by the golden King of Na seal unearthed in 1784, granted by the Han emperor to emissaries of a polity in Kyushu in 57 AD. This trend continued through the 3rd century, when we have the first Chinese historical record of Japan (Wo) saying the Yamatai (Yamato) state under Himiko sent emissaries to China and received the title "Queen of Wo Friendly to Wei" (親魏倭王). The royal titles "king" and "queen" are understood to be subservient to the Chinese emperor (huangdi).

In the seventh century, Prince Shotoku sent emissaries to China in order to emulate the forms of superior government. Interestingly, in spite of their purpose, the message that the emissary carried to the Chinese emperor was carefully crafted to place Japan on the same level as China:

"The Son of Heaven where the sun rises [Japan], to the Son of Heaven where the sun sets [China], may good health be with you." (日出處天子致書日沒處天子無恙云云)

The emperor of China was said to have been greatly displeased by this insolence, but as he was waging war against Goguryeo (a Korean kingdom), nothing untoward came out of this exchange, and Japan kept sending emissaries until the ninth century. During this time, the Chinese recorded these emissaries as presenters of tribute, but Japanese sources treat these as voyages of trade and diplomacy between two equal counties.

In the 10th century, the Song dynasty adopted a more laissez-faires attitude about trade, while Japan likewise allowed its traders to go to Song China. Private trade on the China Seas flourished as a result, with Chinese traders bound for Japan gathering at Hakata (present-day Fukuoka), and Japanese traders stopping by the Zhejiang province in the other direction. The loss of northern China to the Jurchens only accelerated the maritime trade as the Southern Song could only cover their loss of agricultural lands by mercantilism. When the Mongols descended from the steppes, the Japan trade was seen as such a lifeline to the Southern Song that the Mongols tried to invade Japan to put a stop to it.

To intimidate the Japanese, the Mongol Yuan used the old Chinese rhetoric: The Yuan now possess the Mandate of Heaven and Japan should recognize Mongol suzerainty by sending tribute. The Japanese ignored this, and Khublai Khan sent two fleets to invade Japan. This can be viewed as an instance of China (being represented by the Mongol Yuan) actively trying to vassalize Japan, but the kamikaze put an end to that. The Mongols eventually managed to conquer Southern Song without subduing Japan, and contrary to the enmity between the two governments, private trade between the Yuan and the Japanese continued unabated.

The Ming dynasty, which replaced the Yuan, changed all that. The founder of the Ming dynasty, the Hongwu emperor, was concerned with bringing order to China after ousting the Mongol Yuan dynasty. At the time, Japanese pirates took advantage of the turbulent Yuan-Ming transition to raid along the coast of China. The coastal population would sometimes co-operate with these pirates, or to band themselves up for collective defence, and becoming pirate themselves in the process. Hongwu had to clean this up quickly, so he set up coastal guards and fleets to put down the pirates, and decreed that no one except the government build ships. These were the start of the maritime prohibition laws, and private maritime trade died. Hongwu didn't stop there, he even sent Japan a threat to clean up their act and do something about the pirates or else. It is possible that Hongwu even planned an invasion, but in any case Japan under the Ashikaga shogunate complied, since it wanted to re-enter Chinese markets through the only legal channel (tributary trade). They sent some captured pirates to China where they were executed. This was a tacit acknowledgement of Japan's tributary status. When Zheng He went on his treasure voyages to demand acknowledgement of China as suzerain from places as far as Sri Lanka, he didn't go to Japan, but if he had it's not hard to imagine that he would demand its formal submission if the fleet went there.

In the 16th century, the Ashikaga shogunate declined in power, and the right to send tribute to China was contested by the Hosokawa clan and the Ouchi clan, culminating in a 1521 brawl in the Chinese city of Ningbo that spiraled out of control, burned down the neighbourhood, and sank a Ming ship while getting away. The Ming banned Japan from coming to China after this episode, and from here on no official trade was carried between China and Japan until the 18th century. During this time overseas trade was done illegally through smuggling, which gave rise to the most violent forms of the wokou piracy phenomenon.

As a final note of China trying to impose its worldview onto Japan and how the Japanese emissaries tried to please both sides, we can look at the ceasefire negotiations during the Imjin War in 1593, when Hideyoshi tried to invade China through Korea. Ming China expected Japan to seek vassalage so Sino-Japanese trade could resume, while Hideyoshi's demands show that that he saw Japan on the same level of, if not above, China. The negotiators from both sides had to make compromises for these conflicting worldviews, and in the end they had to deceive their superiors. In the end, Ming China acknowledged Hideyoshi as King of Japan and sent Hideyoshi a gold seal indicating such, and Hideyoshi was happy to receive it until he realized what this actually meant, and that his demands were not acknowledged. War was back on the menu.

During the Edo period, the Tokugawa shogunate did not recognize the suzerainty of China over Japan, and so the two countries have no formal relations with one another. However, they had recently taken over Ryukyu (Okinawa), which was a Chinese tributary. This proved to be useful for Japan, and they took great pains to disguise the fact that Ryukyu now belonged to Japan, so that China would still consider Ryukyu as part of its tributary system.