Todd Miller from Impartial Review asked that question a year or so ago in the Google News Help forums and Google said no back then.
Google News representative Harvey said, "You're correct our crawler won't index urls that start with https. You can see the full list of our URL requirements at the Help article linked to below." The link to the article he is referencing no longer works.
Todd believes Google News can now index and rank HTTPS URLs. It is hard for me to verify this without knowing a specific news site that uses HTTPS by default.
I see no reason why Google News can't index HTTPS URLs although I see no reason why they shouldn't have been able to last year.
Top contributor Chris said:
I can't find anything saying that you can't use https for Google News pages, and I know that, by accident, some articles on my site were indexed as https - so I'm thinking they will - but I can't say for sure.No response from a Googler yet but do you know if Google News indexes and ranks HTTPS URLs?
Update: Lyndon on Google+ shared that I can use the inurl:https://www. operator to find them and there are indeed a few https URLs indexed in Google News. But just a few.
Source : http://www.seroundtable.com/google-news-ssl-15573.html
