No. Given only a set of pairwise distances, there is no way to discern whether or not those distances actually reflect reality, or represent any kind of useful measure.
Suppose you give me a set of pairwise distances and want to know if they are good or not. Regardless of the distances you gave me or anything about their distribution or numeric values, I could tell you that the distances perfectly reflect "similarity" as I'd like to define it, or I could tell you that your result was actually computed from random numbers and is totally useless as a measure of similarity. As a very simple example, suppose I tell you the distances between Cities A, B, and C - nothing about those numbers can tell you if those distances are accurate or not. At best you could evaluate if you even have a distance metric or not (like if we find that the A-C distance is greater than A-B plus B-C).
If you have some kind of sample labeling, you could compute some clustering metrics like the silhouette, leveraging the cluster assumption that samples of the same class should be "more similar" than samples of different classes. Here, the class label is used as a sort of gold standard, though, as it's being used as a measure which the derived distances should match. Without any clue as to which samples should be more or less similar, we have no means of evaluating the accuracy of the distance metric.
