Each cluster center is a point in the dimensional space with as many dimensions as extracted factors from your PCA. The row you report is the value of one dimension for each of the cluster centers. If you want to report on the position of the cluster centers, then you need the full coordinates. It is misleading though, to say that a factor "influences" a cluster, as the clusters are built based on factor values, in other words there would be no clusters if you did not start out with those factors.
Whether 0 is a special position for a cluster center depends on the nature of the input variables, but even if you assume that 0 represents mean and median for the values on this dimension it is informative. To give an intutiive demosntration why a value of 0 is informative: imagine a cluster analysis based on a one-dimensional variablwe and you learn that the cluster centers are located at -3,0, and 5. Then you know something about the relative position of the cluster centers. If you ignored the factor you could not even describe the middle cluster.
I think the question might be motivated by the practice of dropping small factor laodings when reporting the results of PCAs, which is offered by some statistical packages (and of dubious value in many practical applications).