Perhaps. But it seems more likely to me that Sauron can't or won't create new Ringwraiths without The One on his finger. Perhaps he would have less control over them, and he certainly doesn't want a rival!I take the fact that there are only 9 Ring-wraiths as 'evidence' (in an absence of evidence way) that the Dwarf rings do not confer immortality and 'wraithyness' on Men.
Also, there may not be so many good candidates for wraithification in these sadly watered-down latter days. Wraithifying some random guy would probably not create anything like another Witch King, who was powerful and commanding even before he got his Ring. And those who are powerful are more wary these days, too. Sauron might have given it a go with Saruman, if he'd had the chance, but I suspect Saruman would not have accepted a Ring from him. Saruman was definitely a potential rival; he did not want to be a servant or a tool.
Perhaps Sauron wanted to hang on to all the Rings he could, in the absence of The One, for some reason on which Ringlore is silent.
I think the evidence is truly absent for answering any of these questions.