This answer will approach the question by focusing on a more narrow case:
"In a conventional wing + tail configuration, is it possible for an aircraft to be stable even if the tail is creating an upforce rather than a downforce?"
The Center of Lift (or Center of Pressure) is the point where we can treat the wing's lift vector as acting, without having to also apply an additional pitching moment to account for a cambered airfoil's inherent nose-down pitching tendency.
The Center of Lift is not fixed-- a point that is not obvious from the diagram in the original question.
If we choose to use the Center of Lift as the pivot point in a pitch torque calculation (which is a valid choice), we are relieved of having to directly account for the wing's lift force in our calculation, but we do have to recognize that the Weight vector, while constant in magnitude (at least if we confine our calculations to the 1-G case), does not act at a fixed distance from the Center of Lift, and thus the nose-down pitching moment due to Weight is not constant. Therefore the situation is much more complex than the diagram in the original question implies.
The Center of Lift moves forward as we increase angle-of-attack and moves aft as we decrease the angle-of-attack. The Center of Lift can even be located beyond the physical edges of the wing itself.
This makes it more intuitive as well as more convenient to treat the wing's lift vector as acting at a fixed point called the Aerodynamic Center of the wing, while also applying an additional nose-down pitching moment which is airspeed-dependent (i.e. the pitching moment coefficient is fixed but the resulting nose-down pitching moment increases as airspeed increases.)
But since the original question takes the Center of Lift approach, we'll do the same in this answer.
Since the Center of Lift migrates forward as we increase angle-of-attack and aft as we decrease angle-of-attack, the aircraft will tend to pitch up as we slow down and will tend to pitch down as we speed up. This is destabilizing-- it is the reason that we need a horizontal tail. But must the tail always create a downforce in order to allow stable flight?
At any given airspeed, if the CG is behind Center of Lift of the wing, the tail must create an upforce rather than a downforce. Since the Center of Lift moves forward as we increase angle-of-attack, it follows that as we experiment with increasingly aft CG locations, we'll see the tail create an upforce at low airspeed before we see the tail create an upforce at high airspeed.
The Center of Lift of the wing should not be confused with the aircraft's Neutral Point. The Neutral Point is the point where the aircraft has no static pitch stability. If the CG is ahead of the Neutral Point, the aircraft is statically stable in pitch, and if the CG is aft of the Neutral Point, the aircraft has statically unstable in pitch. The latter case is basically only the realm of computer-stabilized fly-by-wire aircraft that sacrifice stability for enhance maneuverability or enhanced cruise efficiency.
In contrast, many aircraft have lifting tails. For example, many vintage "free flight" model airplanes have large, positively cambered tails. (See for example this image.) Obviously these aircraft cannot be statically unstable in pitch. The CG must still be ahead of the Neutral Point, even though it is behind the wing's Center of Lift.
An argument can be made that a large lifting tail is generally not as efficient as a small neutrally-lifting or slightly down-lifting tail. That argument is beyond the scope of this answer, so we should save further exploration of that for another ASE question.
Also, plenty of aircraft have a tandem wing configuration, in which the tail is actually a large lifting wing.
Here is a good description of an experiment that verified that the horizontal tail was creating an upforce in flight with a Cessna 172 with a CG that was within, but near the aft edge, of the prescribed envelope -- see last two paragraphs of section-- https://www.av8n.com/how/htm/aoastab.html#sec-pitch-equilibrium
Here is another ASE answer that gives a good treatment of the difference between Center of Pressure (or Center of Lift), Aerodynamic Center, and Neutral Point-- What is the difference between centre of pressure, aerodynamic centre and neutral point?
In summation, the Neutral Point is not the point where the aircraft will balance with the tail creating no upforce or downforce. Rather, the Center of Lift or Center of Pressure of the wing (or to be as precise as possible, the Center of Pressure of the entire aircraft other than the tail, including effects from offset thrustlines, drag from floats, etc) is the point where the aircraft will balance with the tail creating no upforce or downforce. It is very possible for the CG to be behind the wing's Center of Lift (or the entire aircraft's Center of Pressure) but ahead of the aircraft's Neutral Point, thus causing the tail to generate an upforce, yet still allowing positive static pitch stability.
The basic requirement for static pitch stability is simply that the tail is flying at a less positive angle-of-attack, or at least a less positive lift coefficient, than the wing. This includes, but is not confined to, cases where the tail is flying at a negative angle-of-attack and creating a downforce. You can read more about it in this section of an outside website-- https://www.av8n.com/how/htm/aoastab.html#sec-teeter .
This related ASE answer is also enlightening-- Do any airplane designs exist that don't involve a flight surface that provides downforce?
