There have been Chinese navy visits to the Mediterranean. You can sail in on international water. (Edit: Nope, it's to narrow)
"Chinese naval ships visit Morocco"
http://eng.chinamil.com.cn/CHINA_209163/Exchanges/News_20918...
You cannot get into the Mediterranean without passing through territorial waters.
Grabbing for straws: "Chinese naval escort taskforce visits Tunisia"
http://eng.chinamil.com.cn/CHINA_209163/TopStories_209189/79...
The United States has not ratified UNCLOS, and regularly claims the right of Transit Passage. In fact, this fact is one of the reasons why Iran claims that the United States cannot enter into Iranian TTW while making a Strait of Hormuz transit - because the US has not ratified UNCLOS, their claim is that the US cannot claim transit passage. For the United States (or any Western Nation) to make the claim that China cannot claim Transit Passage would lend weight to Iran's argument, which you can imagine, they would not want to do.
I do not want to make any assumptions around your specific views on this matter - you may hold the opinion that China could not claim transit passage, however I wanted to interject some perspective that:
1. That may not be universally agreed upon 2. Specifically, the United States and it's allies may not make that argument because it would put them in a negative position for other international disputes.
PRC actions in SCS is not legally against UNCLOS. Reality is, everything PRC does currently in SCS is legally grey area until UNCLOS/ITLOS/UN actually rule against it in official capacity. PCA ruling is essentially a term paper on official looking letterhead drafted by anti PRC lawfare, pretending to be international law. It's one (strong) legal interpretation, but it's not settled case under UNCLOS - UN (which UNCLOS law operates under) does not recognize or comment on PCA ruling.
Chinese warships will never be allowed anywhere near the Mediterranean in the first place - if there is one thing that even the split US Congress will agree on, it is that China already has too much influence and that they need to be stopped.
Additionally, China's army hasn't seen actual combat in a loooong time. It's likely that their army is in just as bad of a shape as Russia's is, and getting that demonstrated on the world stage before they have a chance to snack a piece or the whole of Taiwan would be pretty foolish.