Yes, Domain Authority will help the rank orphan pages hosted on the same domain. mysite.com/mysubpage
No, they don't help rank a subdomain with no links to it. mysubdomain.mysite.com
Different observation here, just one example, seen it multiple times:
Wordpress.com, subdomain name is Keyword1Keyword2.wordpress.com. Keyword1 and Keyword2 are
no existing tags (=subdirectories) on wordpress.com, so I add posts on my blog using these categories/tags (always all of them to make the content on the tag pages and the blog as similar as possible)
To avoid any falsification of the results, blogroll is empty and no other already existing categories/tags are selected. Now I point links from the exact same external pages to Keyword1Keyword2.wordpress.com, http://wordpress.com/tag/Keyword1-Keyword2/ and http://wordpress.com/tag/Keyword1Keyword2/ to get them crawled, same anchor text.
In most cases, Keyword1Keyword2.wordpress.com will outrank
http://wordpress.com/tag/Keyword1-Keyword2/ and http://wordpress.com/tag/Keyword1Keyword2/ in google for a search for Keyword1 Keyword 2 as well as Keyword1Keyword2.
The only wordpress specific thing to keep in mind: They can kill your blog for a TOS violation, but they won't kill the tag/category, so you can always create a new blog and grab the traffic from the tag/category while the traffic from the deleted blog is lost forever.
The advantages compared to own hosting: For low and often even medium competitive terms, you are very likely to get a google first page result. If a new hype starts or a totally new niche is born, I want two things: Profit from it long term (own domains) AND grab this first wave of traffic (hosting on authority domains).
So, while I build my own sites that slowly gain ranks, the authority domain sites grab the traffic. It's a quick extra income on top. Sure, a #1 ranked wordpress blog with commercial background, especially adult, is gone fast once your competitors spot it...but no matter if it lasts a day or even weeks, months, it's alot of $$$ for almost no work. I had blogs on wordpress that made me net around $1k in a week. Sure, kicked, but I'm still farming the tags with new blog.
I just like the idea of diversifying, the main focus is on my own domains, but whenever I spot an opportunity, I'm all over wordpress, blogger, squidoo and other authority sites to grab my share. It's not like it takes long to fire up a site there, plug your own domains in the blogroll, add a few posts, that's it. If they last, even better, free links.