Yes, but they don't create battery technology, they use batteries designed by others.

They don't manufacture their own cells (why would they?) but the battery pack is their own design [1] and what sets them apart from other EVs:

    The battery pack in the Tesla Roadster is the result of     
    innovative systems engineering and 20 years of advances in 
    Lithium-ion cell technology. Tesla's ingenious battery 
    pack architecture enables world-class acceleration, 
    safety, range, and reliability. The non-toxic pack is 
    built at Tesla’s Headquarters in Northern California.

[1] http://www.teslamotors.com/roadster/technology/battery

Exactly. But they are still limited by advances in the underlying battery technology, which they did not invent.