Yes I believe that you can detect a Force sensitive even while asleep... there are a few ways to detect them... One of them being the Midi-chlorian count...
Let's say you have a sleeping person and you know that there was a Jedi / Sith presence in the area... If you really wanted to you could go around testing people's blood for the presence of Midi-chlorians..
One person actually commented on my answer to the question...
How do the Jedi find Force-sensitives?
In one of the books (Thrawn?) they discover a device which can read
force sensitivity from a person. Maybe that device can just remotely
detect Midi-chlorians. – Jack B Nimble 2 days ago
I don't think the user of the Force can hide the presence of the Midi-Chlorians in their blood so this is a way to detect Force sensitives even while asleep...
There is also this..
In Leia's quarters in the abandoned Emperor Palpatine's Imperial
Palace on Coruscant, Luke and his twin sister Leia Organa Solo were
doing some tests on the inner defenses of her brain. Luke was using
the Force to access certain areas of the brain; as he accessed an area
in the very back of the brain, he was rebuffed. They confirmed this to
be a natural reflex of the Force-sensitive.
The above mentioned quote is from post Star Wars movies. So even if a Force sensitive user is asleep, if somebody tries to use the Force to access certain areas of a person's brain and get rebuffed then they are a Force user.. I believe since it states it is a natural reflex even while asleep this reflex should still be active.