Only if you use Dual_EC_DRBG. Bitcoin doesn't use it, or any other PRNG for that matter, instead relying on the OS's entropy source, which (normally) produces random numbers from hardware sources. Note that ECDSA (which Bitcoin does use) is not related to Dual_EC_DRBG in any way other than being based on the elliptic curve discrete logarithm problem, and does not have this backdoor.