In the open ocean? Yes, that's what nuclear submarines do. Nuclear submarines sail fast simply because they can, and they can because they have infinite fuel.Do you believe 093B was sailing with speed 30 knots for 5 days continuously?
Alternatively, it's possible the sub loitered around the Ryuku island chain for a few days to get a feel of JMSDF operations tempos. If that's the case, I wouldn't be surprised if the JMSDF were tracking the sub for as long as it was within proximity to the Ryukus. But I also would expect the captain to know he's in vulnerable shallow waters heavily patrolled and monitored by an adversary nation so it's important to not reveal wartime acoustics signatures while he's in that zone.
The sub 093B could not run away from JMSDF's destroyer Onami. Onami's max speed may be about 30 knots. Perhaps, 093B's max speed may be slower than 30 knots.
The chances of a destroyer stumbling upon a submarine in the middle of the Pacific Ocean are a few million to one. There is no way the JMSDF were tracking the 09III until the captain made the conscious decision to sail within close proximity of the Ryuku island chain.