Theoretically, if the Neutral Point was still aft of the C of G with the tail gone, you could still be statically stable to some degree, but without the trimming surfaces of the elevator/stab providing the pitching force-balance system to control AOA, you become statically stable about the wing's zero-pitching-moment AOA somewhere, and you are more or less a lawn dart or a bomb and will arc down until in a statically stable vertical plunge.
You are unlikely to be able to make the wing, as it is, provide the required trimming power that was being provided by the tail. You might get some pitching authority by making the existing ailerons work together as elevons, but amount of pitching/trimming power would be so limited, it would only give you some control over your impact point, like a laser guided bomb, or at best, make it possible to maintain level flight at very high speed.
For that kind of concept to work, you would need to effectively reconfigure the aircraft as a flying wing, with all of its limitations, by incorporating all of the required pitch control and trimming authority for the full flight envelope into the wing itself, which means you have to design a new one, with a different airfoil and appropriately sized elevons at the wing tips, a limited C of G range, and all that sort of thing.
Then, on to your flying wing you stick a fuselage extension with a tail surface, for which you must also add fuselage forward to balance out, and you have a kind of weird hybrid tail-less-airplane-with-a-tail, like the evil genius farmer who bred a cow-chicken hybrid to provide a unified solution to eggs and milk production.