If I understood your question correctly, you are performing multi-class classification with an SVM at hand, but, are calling/viewing this multi-class setting as clusters. Which then explains your use of the terms 'distance to the cluster (center)'.
"... 'distance' of the data-item from the cluster."
My answer to your question
if the approach of taking the probability generated by SVM will be correct as a proxy for the distance measure
is: No. Read on for the 'why' part.
In my opinion, to answer your question, briefly recounting SVMs as against clustering should help. SVMs work with separating hyperplanes, because it has the knowledge of the class-labels beforehand. On the contrary, any clustering technique, in absence of this knowledge, looks for cluster centers and hence is bothered about the distance of any data point from its corresponding cluster center. The hyperplane is nowhere giving you information about where this cluster center lies, so, it won't be correct to use the confidence measure from SVMs as a distance measure from the cluster center, certainly not for estimating the class cohesiveness. This could rather be done by visualizing the class/cluster if that is possible. Distances between data points can not be known from SVMs directly, all it can tell you is w.r.t. the learnt separating hyperplane -- which side of the hyperplane and how far from it.