Anti-access is potentially a winning strategy against the United States. The Chinese would be unlikely to gain anything more than momentary or surprise success against an American naval aircraft force at sea, but would be likely to present sufficient threat to make any U.S. attempt to maintain a strong naval force close to Taiwan dangerous.
The only exception to this is American submarines. American submarines likely have the capability to attack and sink any ships the Chinese decide to sail. While the Chinese have developed anti-submarine warfare techniques (and practice them routinely), it is unlikely that they are of sufficient skill to prevent submarines from attacking Chinese naval surface forces. However, by using a bastion defense strategy along with other anti-access tactics, it may well be possible for the Chinese Navy, Air Force, and missile forces to at least delay entry of submarines (and surface ships) into the Taiwan Strait long enough to make any further attacks either impossible or too costly.
For further reading on this, see:
China Naval Modernization (Congressional Research Service)
China's rising seapower
The Chinese Navy
and, thanks to Chris Dixson, this piece from RAND