I have objections to that plan. Usually, SSL configuration for web is more involved, and more security risk prone, which means updates sometimes. This would result in multiple components getting updates.
Another issue is the incompatibility between the OpenSSL configuration (usable only by the web component for the forseeable future) and the JSSE configuration.
So I don't see much sharing. Or to put it another way, there's a lot of sharing possible for everything *but* the web component.