Forum Moderators: Robert Charlton & goodroi
You may well smack into all the other ranking obstacles that can confront any site that renames their URIs in other ways (html to htm, www and no-www, etc.) Content that is indexed with both protocols creates a duplicate issue for Google to sort out. The new URIs will also be "new" and have no history going for them. If your site is long established, this factor also can create ranking issues.
I know of one site that accidentally resolved all their URIs with both https and http. The http versions were indexed first. When the https versions were later indexed, those were the ones that stuck in the Google index and the http versions became Supplemental. That was a horror show for them (their rankings completely tanked), but could be what you prefer.
That experience was pre-Big Daddy, but it shows that troubes are possible. You may want to use the <base href=""> tag in the head section of every document to show that you intend the https protocol to be used for every navigational link in the site.