OpenSSL's ECDSA implementation does not use Dual_EC_DRBG.

You can read about what is actually done to make ECDSA keys here.

https://wiki.openssl.org/index.php/Creating_an_OpenSSL_Engin...

None of this has anything to do with ECDSA. Dual_EC_DRBG is a random number generator, not a signature algorithm.