Some idea not properly checked.

fullTextEntityManager.getSearchFactory().disableIndexingFor(fullTextEntityManager); //or entiityManager
fullTextSession.getSearchFactory().disableIndexingFor(fullTextSession); //or session

Then the underlying disabled session could be extracted from the FullText* objects and stored by FullTextIndexEventListener. The EventSource happens to be that session object and we can do an == comparison.
Now the difficulty is how to keep this list of sessions and have it properly garbaged collected. Since there is not Session close hook event, I supposed we could reuse the same approach used for FullTextIndexEventListener.flushSync.
I am not quite sure why this one is thread safe but I supposed that it's because the same thread which sets the value also reads it. Which is our case here too.