I would say , nope !! Lol. I think you are doing the right thing ! Let him cry ! I use the white noise too and fans . So I don't get frustrated but they have their naps . I have a lot of 3 day a weekers . My one dcg , 21 months does not nap or sleep for mom , up until 11:00 or so , doesn't bother me here , she only came one day this week ( due to sickness ) and she cried for the first 1/2 hr of sleep but she finally fell asleep woke up an hour later and I still let her cry , she fell back to sleep and ended up sleeping until 3:30 . As long as consistency is followed at your house what happens at home can be overcome !!!
Good luck to you !!!!!