Wouldn't the asymptotes of the 2D projection of the inverse of the Riemann Zeta function show the real part of all the non-trivial zeros?

Can somebody provide a visualization of $z=\frac{1}{\zeta(x+iy)}\pm N$ for some large $N$ projected onto the $xz$-plane? I would imagine that if we found any asymptotes converging anywhere other than $x=0.5$ it would disprove the Riemann Hypothesis. This is just a hypothetical idea I had and so I was wondering what complications or flaws there are with this reasoning.