I'm not sure whether the phrase has a typo in it or not because I couldn't find the proper translation from MDBG, Ichacha or Ichiba. However, I did find an example:
China’s 5000 year history, the variety of its customs and cultures, and its general mystique, have always pulled on the hearts and imagination of westerners.
I take '遐想连篇' here means making you imagining or drawing your imagination out.
I'm not sure I got the correct meaning though. I think sometimes it doesn't make any sense. For example: 'Pulling (your) imagination' make sense in 让人遐想连篇的小说, but not in 让人遐想连篇的话语
Do you have a better way to put the phrase '遐想连篇' in english?