 Solution

No: with one pair per stratum, the statistic uses failure order but discards the size of the time difference. The paired log-rank reduction to a sign test assigns the same contribution when A fails just before B as when A fails much earlier. This deliberately avoids a model for the failure-time distances, but it does not extract every kind of evidence in the recorded times. An accelerated failure time model, for example, could use log-time differences in uncensored pairs under additional distributional assumptions.