Yes it can and did, but not fully successfully.
Three SR71 missions were tracked/fired on during 1967/68 and one was hit by fragments from a detonation in the rear quarter. This damage caused a change in employment of these aircraft. That a 'near-miss' was recorded from 3 engagements suggests that Dvina can track and hit the SR71, but the hit probability and window of opportunity is very small due to the relative performance of the missile, the later Volhov has several improvements in missile technology and guidance/tracking modes that improve the chance.
The shot must be taken at extended range to avoid the steep energy burning climbing turn, it can easily be defeated by a change of intercept point by a target change of course, and missile manoeuvring potential at long range/high altitude is poor. There is zero chance of catching and shooting down a receding target - so once the 'early' aim point is passed the system cannot fire with any kill-chance.
You need to 'place' the missile ahead of the target and allow the target to intercept the missile, rather than the other way around... Volhov and Dvina are similar in their ability to achieve this.