link and compile do not work together, no.

In the directive definition object, if you only define link, that’s like shorthand for having an empty compile function with an empty preLink function with your code in the postLink function. As soon as you define compile, link is ignored by angular, because compile should return the linking functions.

If you only return one function from compile, then it’ll be executed post link.

Or, put differently, link is just a shortcut to the postLink function that gets called after the scope has been linked by compile.

It’s (sort of) documented here – look at the comments in the code sample.