I travel all over the US for business and I find that geographically there are certain women or agencies that cater to late night appointments, just as those the have day time schedules. I prefer the late night outcall to my hotel, but if I have seen the provider before, I will go to their incall for a late night tryst.
To me, and I hope I don't lose my man card here, the late night appointment is more romantic rather than the daytime rendezvous. Heck I didn't even entertain the idea of daytime meetings until I moved back to Texas!
You should do just fine at night, but as stated, keep up with your screening.