You're talking about power projection capabilities. No, PLA currently does not have much of that capability beyond first island chain against a world class opponent (really, only the US).
PLA's primary focus over the last two plus decades has been homeland defense, Taiwan contingency and more recently South China Sea. Over that time, China has now acquired the capability to dominate within the first island chain.
Without the repeated US challenges to its territory and sovereignty, China would probably have not invested as much in various defense technologies and platforms, not so soon anyway. During the 1995-1996 Taiwan crisis, the US sent two aircraft carriers to the east of Taiwan to show deterrence. That prompted China to develop the ASBMs, resulting in DF-21D, DF-26 and the associated C4ISR capability. The 2001 Hainan Incident had accelerated the investment and development in the defense facilities on Hainan and in and under SCS. The US came up with its AirSea Battle doctrine to counter China's A2/AD strategy, or the other way around. With the growing disadvantages in its AirSea Battle strategy, the US began to pivot to the third Offset Strategy, backing away from 1st island chain and overcome the distance problem with long-range and stealth weapons. More recently, realizing its disadvantages in conventional mid-range ballistic missiles against China, the US withdrew from INF treaty and wants to develop conventional mid-range missiles and deploys them around China.
The US keeps coming back with new doctrines to threaten and deter China, while PLA keeps growing in capabilities to counteract these new threats. In the end, we'll find out that if the US can't stop its hegemonic behaviors toward China, PLA will have keep growing, first to dominate the 1st island chain, then to gain superiority in West-Pacific and Northern Indian Ocean Region, and eventually to go toe-to-toe with the US globally, just to protect China's territorial, sovereign and development interests.
Over the next decade, we'll see China obtaining all the key power projection platforms and capabilities, from CATOBAR aircraft carriers, the next-generation SSN and SSBN, the long-distance stealth strategic bombers, a large fleet of military transport and tanker aircraft, to a fleet of amphibious assault assets. These are backed by China's burgeoning space-based C4ISR capabilities. There will not be any technological or financial barriers to form a formidable power projection capability, as long as the needs exist.
So, China might not have felt the need to develop world-class power projection capabilities if left on her own, but the current hegemon and its vassals are so entitled to their privileges and dominance such that they would do anything to suppress and contain China. China has no other choice but to develop the capabilities to counter. In the process, PLA will accidentally become a formidable global military power by mid-century. That's the goal CCP sets out anyway.