That sounds about right. Keep in mind that in "The Naked Time" that it was less than 20 minutes to hit the atmosphere, so they might have been a little higher up or moving much faster than a simple hover...
If you cut the engines, while the Enterprise is hovering at 200 miles, she would hit the ground in 4 minutes and 16 seconds. From maximum transporter range of 16,000 miles, she would hit the ground after a leisurely 38 minutes and 11 seconds. Both times assume no atmosphere, I'm afraid I can't quite figure that out.
Twice the distance (in meters) divided by 9.81, the square root is your time in seconds.
The Captain's Log in Naked Time said they had nineteen minutes left. But that was a while after Riley cut the engines.
There might be occasions when they're mapping a world where the ship would be in orbit.