No, it is not.

Using sage, format is
n-th zero, zero, Re(zeta'(s)):

```
127 (0.5 + 282.46511476505209623j) -0.051786600288820422906
136 (0.5 + 295.57325487895829239j) -0.031941907138887597722
196 (0.5 + 391.45608356363804577j) -0.047584869480501458447
213 (0.5 + 415.45521499629459886j) -0.57814342438306688421
233 (0.5 + 446.86062269642952253j) -0.27263428500279642628
256 (0.5 + 478.94218153463482654j) -0.12771720375134527005
289 (0.5 + 527.90364160127234523j) -0.96196701578032407318
368 (0.5 + 637.39719315983730717j) -0.31309354934078881436
```

Code:

```
import mpmath
for n in [ 1 .. 1000]:
z=mpmath.zetazero(n)
d=mpmath.zeta(z,derivative=1).real
if d<mpmath.mpf(0): print n,z,d
```

**Added**

As Joël reminds, sage is free software.

You can even use it in a browser on:
https://cloud.sagemath.com/

As an optional package it contains a database
of zeta zeros at http://sagemath.org/packages/optional/
Check: database_odlyzko_zeta.spkg

This is OEIS: https://oeis.org/A153815

A153815 Numbers of nontrivial zeros of Rieman Zeta function where the real part of Zeta'(s) becomes negative.