I suspect that may be possible, or (me being a bit of a technological luddite) possibly a graph for any given aeroplane which can be referred to before take-off and says for runway length X and headwind Y in this aeroplane, below height Z you will not get away with a turnback, but above that you have a fighting chance if flown well enough.
G - Yes a good theoretical experiment, that may yield some interesting and anecdotal information reference said aeroplane. But that is the point, it will be that particular aeroplane, with a particular weight, with a particular configuration. The concern Backpacker was alluding to, correct me if I am wrong BP, was that someone MAY, read this, and think, I am going to try that next time I take off in my PA28 or whatever, and guess what - the 45 degree bank angle et al might not work.
This is Bonanza specific. You fly landing approaches at 1.3 times stall speed (good compromise between low speed and safety margin above stall. Therefore in a 45 degree bank angle, multiply the stall speed by 1.3 and you get a turnback speed with same safety margin for stall - app Vy.
Also, which I do not think anyone has pointed out yet, high density altitude airfields make this almost impossible because the climb gradient is flatter, and high weight also reduces climb gradient which in turn raises your stall speed, and turn speed, which increases your turn radius and decrease your rate off turn.
Let your watchward be take care.