China doesn't need to go to the Atlantic. If she wants to establish persistent and credible carrier presence west of Guam during period of international tension, she would have problems doing so without nuclear power or a large and vulnerable fleet underway replenishment capability.
China can deploy throughout Indian Ocean to east coast of Africa in peace, yes. But she would also have a great deal of trouble keeping up conventional logistic and fueling support for any forces there during international tension.
So if her strategy calls for her to sustain credible naval carrier presence more than, say 2000 NM from Chinese shores without first acquiring offshore bases, she would likely need something akin to an all nuclear task force.
I feel people quickly overlook that an all nuclear task force still is limited by food, water, and ammo supplies. Fuel as well if we're talking about planes, helos, and amphibious gear. Aside from the sensors and armament retrofit on the nuclear cruisers costing too much, I think the USN stopped going nuclear with the ABs because of these factors. For a smaller tonnage like the AB (vs carrier), the benefits of nuclear don't overwhelming overcome the limitations of the other factors. USN is still heavily dependent on oversea bases, ports, and replenishment vessels.
I would make the counter argument that going to the Atlantic would help China's maritime strategy in many ways.
1) You don't lock in all your naval assets only in one hemisphere.
2) You establish relations with countries bordering the Atlantic that may be very useful in terms of trade and diplomacy. South America comes to mind.
3) You can potentially tap into the weapons market in that part of the world when you routinely demo your products in the form of visits.
4) You can blunt the American pivot because it would mean they need to reconsider their Atlantic interests. The pivot relies on redeploying portions of their forces from the Atlantic.