In its initial run, or The Producers), it was never really dependent on its star for business; when Zero left, it still sold out. Dolly's business tended to depend on who the lead was. Not so, Fiddler.
It did go on to become the longest running show in Broadway history, back when Times Square was as uninviting as it probably ever has been, when tourism was pretty minimal (there were always well-to-do out-out-of-towners, but their numbers paled in comparison to tourists today), pre-internet sales, pre-credit card sales, pre-TV advertising. It really was a phenomenon in its day. I was a kid at the time, and remember being annoyed that it had dethroned HD, because I enjoyed HD much more (I probably was too young at the time to truly appreciate Fiddler).