domain authority and long tail keywords

Does domain authority spill over to pages and affect rankings for long tail keywords for specific pages?

In my experience it does. Look at Amazon - domain with high authority, subpages ranking for all possible keywords, without any links.

I know a lot of people will say PR is something not to worry about...but I do believe it helps rank several long tails that you may not even be targeting

Definitely think there's strong correlation between a high DA and long-tail visibility. In fact, I'd go as far to say that there's causation as well.

Best thing to do though, once your increasing DA gets you exposure to those keywords, is to check your analytics for incoming long-tail keywords that are converting at a high rate and try and optimise for them outright.

A short question to your question is yes. I have done case studies on that. Here is a sample case study, all these urls are ranking #1 on their respective long tails with few or no backlinks. You can verify by googling the longtail in the url. The domain is high Authority.