Is there an option to view what percentage of questions in a community have an accepted answer?
If you can live with data that is at maximum 7 days old you can use The Stack Exchange Data Explorer to query for that data.
I've created this query that uses a small generating query to create a query that runs across all databases and is an union of this query:
select (select count(*) from [StackOverflow].dbo.posts where posttypeid=1 and acceptedanswerid is not null), (select count(*) from [StackOverflow].dbo.posts where posttypeid=1), 'StackOverflow'
This is the top 10 of communities with the highest percentage of accepted questions, at the date of posting:
site |# Accepted |#Questions |Perc Puzzling |1476 |1855 |79,5687331536388 Spanish |1610 |2124 |75,8003766478343 German |3527 |4662 |75,6542256542257 Rpg |8409 |11406 |73,7243556023146 French |2018 |2744 |73,5422740524781 Japanese |4272 |5812 |73,5030970406056 Russian |838 |1185 |70,7172995780591 Boardgames |3525 |5045 |69,8711595639247 Homebrew |2408 |3563 |67,5834970530452 Outdoors |1204 |1786 |67,4132138857783
Sure, this is possible using the built in search of every site.
For example on MSE itself:
Gives 0.496 which is 49.6% questions with accepted answer.
Worth to warn that the "answered" percentage that can be seen in the full list of sites is not related to acceptance, it means questions with at least one answer that has positive score. (88% answered for MSE for example)
On this link, you find an overview of all sites, the amount of questions, the percentage of questions answered, and more.
Camil Staps answered this and then deleted it, however I appreciate his response.
The percentage answered figure is the proportion of questions that have an answer with a positive score or an accepted answer, not just the questions that have an accepted answer.