Hosting CiviCRM and Wordpress on WPengine
I have a couple of test sites running on WP Engine.   Mostly to fix an issue that came uo in CiviCRM 4.7.x.   I have installed and configured 4.6 on WP Engine.   My only issue had been they used to have many sites on php 5.3.3  but I am mostly seeing 5.5 these days.   I know CiviCRM has some issues with HHVM, so you would need to verify that your client site is not running that.  I have not used WP Engine in production yet.