Yes. Though the test would only tell you that the other side has at least a few working nukes, not the proportion of working nukes.
(If a side could credibly commit to testing an unbiased (pseudo-) random sample of nukes, they would be able to convince the world that a large portion of their nukes work.
But I am not sure how you would do that without revealing all of your nukes?)
(If a side could credibly commit to testing an unbiased (pseudo-) random sample of nukes, they would be able to convince the world that a large portion of their nukes work.
But I am not sure how you would do that without revealing all of your nukes?)