Short answer: early evidence says yes. In adults with major depression and suicidal ideation, a randomized trial in the American Journal of Psychiatry reported that starting low-dose buprenorphine about 48 hours after a single ketamine infusion was associated with a larger and more sustained reduction in suicidal thoughts over four weeks compared with ketamine plus placebo.
Both groups improved quickly after ketamine; the added benefit of buprenorphine appeared specific to suicidal ideation, not overall depression severity. No serious treatment-related adverse events were reported at the low doses used in that study.
The trial was small with short follow-up, so dosing, durability, safety over time, and generalizability remain uncertain. I cannot verify more than what is described in the published report.
In sum, low-dose buprenorphine after ketamine may prolong anti-suicidal effects, but the evidence is preliminary.