The short answer would be that its highly unlikely they would have succeeded.

While the Japanese did indeed experience an outstanding success in the beginning of the war against the Koreans, this owed most to the lack of preparedness among the Koreans, and their lack of experience with modern infantry tactics. Namely, the Koreans used neither cannon nor firearm, and here hopelessly outmatched against the Japanese troops. For this reason, without Chinese intervention, Japan could feasibly have taken Korea and consolidated without major issues, provided they dealt with the Korean navy under Yi Sun-shin.

Now China is a completely different ballgame. Chinese armies were on another scale than Japanese ones, numbering in the hundreds of thousands. Chinese armies were also battle-hardened and experienced, having fought domestic wars as well as conflicts against Mongols in recent years. China used cannons and firearms as much as the Japanese, and as some historians like Samuel Hawley ahve argued, they applied cannons in the battlefield in a manner that was more sophisticated than the Japanese. As soon s China got involved int he conflict, the tide of war was turnerning against the Japanese. It wasn't a blowout by any means, the Chinese had to fight for every inch, and also suffered setbacks. But Japanese progress was effectively stifled.

The other argument why the Japanese would have failed, is the sheer size and scale of China, which far outnumbers that of Korea. The Japanese army was not logistically strong. Perhaps a more potent failure was the Japanese failure to consolidated the territory they conquered. Even as they conquered Korea, they failed terribly at administering it with any sense of normalcy. Arbitrary brutality and lack of interest in administration firmly turned local Korean populations against them, and partisan groups of "righteous armies" were common, and they helped dislodge Japanese control of several provinces.

Although Korea could feasibly be dominated through sheer force without Chinese intervention, doing the same thing inC hina would be hopeless. Lets say Hideyoshi's army would manage a sort of lightning war into China after subjugating Korea, and taking Beijing. Would it be a major victory? Certainly. Would China be subdued? By no means.

The Imperial court could always evacuate to one of the other giant, well-defended Chinese metropolises, like Nanjing, as they did when Beijing fell to the Manchus in 1644. Of course, they still lost the long-term war to the Manchus then. But that was only because the Ming dynasty was crumbling on its own, and the Manchus managed to convince Han Chinese generals to defect to them, as they styled themselves as the legitimate successor dynasty, the Qing.

Nothing in 1592 implied Japan would manage to do anything similar to what the Manchu accomplished. Hideyoshi and his generals had a very low understanding of CHinese affairs, and there is nothing imply they would ahve styled themselves a s a new dynasty, or managed to win over the Chinese population, or inspire defections form the Ming military. No matter how many successes they achieved in the battlefield, the Ming could always retreat and regroup, and eventually the Japanese would be overstretched and forced to give up.

Therefore my final verdict is that China was beyond the reach of Hideyoshi and the Japanese. The best bet of the Japanese lay in consolidating control over Korea, and trying to strike a deal with the Chinese for controlling southern Korea, perhaps in exchanging for accepting vassalhood to the Chinese. But militarily, they were outmatched in the long time.