It is hard to say, because even now there is no standard criteria for electing relievers. I think relievers that came along before the change in strategy have gotten shortchanged, notably Dan Quisenberry. There are a dozen guys like Stu Miller and Johnny Murphy, who are not remembered well because they didn't collect saves, but were just as good as the top relievers today. Since only three relievers have made the Hall (two of which spent part of their careers as starters), its hard to see eliminating the save having a large impact. The leaders already (Lee Smith) are not inducted.
I think voters should recognize a good pitcher from the traditional statistics, and not need saves to make that distinction. Judging from the relievers they've elected at this point, I don't think the save makes an impact.