Not natively, but there may be some usable text script on AEScripts.com...
Has there been any development in this area since CS6?
I've subscribed to the Cloud with the intention of making quality international versions of my clients' productions & so far have to revert to free stuff to finish the job.
Adobe 'should' be able to integrate an import function for .SRT or preferably .*** subtitle / closed caption files without too much ado. I can only assume there is some strategic, incomprehensible reason not to.
*** That's "Advanced SubStation Alpha" (.A.S.S), or homonym for 'donkey'.
I just found this plugin for importing subtitles as an SRT file, and being able to burn-in titles to Adobe Premiere or After Effects (then use dynamic linking to premiere timeline).
I have also seen some scripts where you can import a script to After Effects, and then use dynamic linking to put it into premiere. But I have not been able to get that to work for me. Going to try the plugin next.