The landing abort burn itself should not be the problem. But getting back from an ascending rocket to a descending rocket fast enough seems impossible to me, for two reasons:
A) Remember, that even with a single engine on at lowest thrust level, the rocket would accelerate away from earth. So after the landing abort, all engines have to be turned off. But with a positive velocity (away from earth), the rocket will experience negative g-forces, accelerating it to earth faster than gravity alone would! This is because the rocket in free fall has zero g-force, but with air drag, its movement away from earth is decellerated, meaning, that the rocket is accelerated towards earth faster than by gravity alone!
Negative g-forces have drastic consequences. Whatever little fuel is left at the bottom of each of the two tanks, now suddenly feels, that "up" and "down" have just been reversed, and starts moving towards the new "down", which is, where the "up" used to be! You can simulate that at home in your kitchen easily: Fill a glass with water (your "fuel"), take the glass in a hand, then push the glas up suddenly (the abort burn), then down again (the phase, where gravity wins). Even though you never turned over the glass, the water spills all over, when you do that fast enough!
Of course, the fuel tanks of the rocket are closed, so the fuel will not spill out during the phase of negative G-forces. And the fuel will start flowing back to the bottom, once the rocket has reached its maximum height and starts falling back to earth, because air drag now causes positive G. But will enough "air"-free (more precisely: helium-free) fuel collect at the bottom during the few seconds of free fall?
B) As already written, the rocket might become instable. While going up with engines off, it gets slower and slower, so that it is harder and harder to control by the grid fins. The fuel sloshing in the tanks add to this instability. The thrusters might be able to keep the rocket upright, but I am not sure, if they can.
C) During the non-powered phase of flight, the rocket will hardly be able to offset wind drag. Of course, the rocket could already stear in the right direction to counter wind during the abort burn. But in the case of unsteady wind (which on a nominally performing rocket is the most likely problem to require a landing abort in the first place!) the exact required direction might be hard to predict - and the final correction of the wind shift will be hard.