I've only been to 2 and both times the surprisee admitted later to having an inkling.
It's my, ahem, significant birthday soon, and scenarios are going through my head, that if anyone ever wanted to fool me (not that they would), they'd have a difficult job as I'm naturally sceptical.
I mean, who would believe that all their nearest and dearest were unavailable around the time? 
So IABU to think it's impossible to throw a Completely Surprising Party?