In a half cell reaction, Is the potential halfed? If you have an electrolyte of $\ce{Zn^2+}$ and $\ce{SO4^2-}$ (Neutral) Then you dip in it a Zinc electrode.

Zinc potential is $\pu{-0.74 V}$ (relative to SHE). So that means there is a $\pu{-0.74V}$  difference between the electrolyte and the electrode.

But When you dip in the solution the electrode makes the solution more positive and it self more negative the same amount so the overall potential of the electrode will be $\pu{-0.74 V} / 2 = \pu{-0.37 V}$, and the solution will be at $\pu{+0.37 V}$.

Is this true? (assuming the solution is not connected to any other salt bridge or porous disk)

Edit: Absolute electrode potential is really the difference between the electrolyte and the electrode potential. 

And the question is just this if you have an electrode inside an electrolyte with no salt bridge will it's potential be halfed.
Those $\pu{-0.74V}$ are measured against a standard hydrogen electrode. That's the universally accepted but totally arbitrary standard.

You don't have a second electrode, hydrogen or other, so the absolute number is totally meaningless. If someone had decided to use the zinc electrode instead, as zero point for the electrochemical series, then the voltage you mean would be zero. Makes no sense.

There is an absolute cell potential (absolute electrochemical series), with a different zero point, but it's totally uncommon, because it's very tricky to measure absolute electrostatic potentials of only a few hundred millivolts. I believe the problem is the calibration, while a platinised platin electrode bubbled with reasonably pure hydrogen is probably the simplest reference standard to reproduce at all.