Does Baidu Support HTTPS?

Yes, since 2015.

In May 2015 Baidu publicly announced full support (for processing and indexing) websites using HTTPS.

Prior to this, Baidu recommended that websites created an HTTP and HTTPS version of their websites, so Baidu could process, index, and rank the HTTP version of the site.

At the time of this announcement, Baidu also revealed they would give priority to websites utilizing HTTPS technologies in their ranking:

In order to provide users with a safe and reliable network environment, after enabling https encryption, Baidu search launched again: full support for direct inclusion of https pages; in addition, from the perspective of relevance, Baidu search engine considers sites with the same weight to use https. The pages of the protocol are more secure and will be given priority in ranking.

Baidu Webmaster Platform, May 25, 2015

Given that HTTPS technologies have since been widely adopted by nearly all websites, the proclaimed ranking benefit is now likely null.

As this contradicted previous Baidu advice, they recommended webmasters 301 redirect the HTTP to HTTPS versions of the website to avoid duplication.