Plenty of managers get hired with little to no coaching experience. I don't know the history of pitching coach employment, but I can't imagine teams would be more precious about needing experienced pitching coaches than they are about needing experienced managers. That said, I don't think the Red Sox will choose not to hire Schilling because he's never held a coaching job before. I imagine compatibility with the team's overall plan and philosophies, not to mention with Alex Cora himself (no idea what relationship, if any, the two have), would play a larger role.I'm risking being 126% wrong because I haven't looked, but it seems pretty rare for a major league pitching coach to have never had a job coaching anything anywhere before getting hired as a major league pitching coach.
I expect Schilling's chances are better for getting the Phillies' managerial spot, but even those are slim. Gabe Kapler had some experience as a coach/manager, but not a lot. Bringing in a totally green rookie as his replacement doesn't seem a likely next step.