Does propwash increase pitch stability?
There is not an obvious answer to this. I'll outline three effects (among others):


Placement of thrust line. If the thrust line is placed below the CG, it will have a destabilizing effect; the converse is true. That's why wing mounted engines tend to destabilize aircraft as throttles are increased. But that's not the title of your question.
The local increase in flow from prop wash increases the wing lift slope. This tends to decrease the pitch stability. An increase in lift has an associated increase in downwash as a function of AOA. This also tends to decrease stability.
The local increase in flow from prop wash increases the tail lift slope. This tends to increase the pitch stability.


The neutral point contribution is as follows (cited from Etkins, Dynamics of Flight):

$$h_n=h_{n_{wb}}+\frac{a_t}{a}\overline{V_H}(1-\frac{\partial\epsilon}{\partial\alpha})-\frac{1}{a}\frac{\partial C_{m_p}}{\partial\alpha}$$

where $h_n$ is the location of neutral point, $h_{n_{wb}}$ is the wingbody aerodynamic center (AC), $\overline{V_H}$ is the tail volume with respect to the wingbody AC, $a_t$ is tail lift slope, $a$ is the total aircraft lift slope, $\epsilon$ is downwash on the tail, $C_{m_p}$ is the pitch moment contribution from thrust.

Forget about thrust line for a moment, then we have:

$$h_n=h_{n_{wb}}+\frac{a_t}{a}\overline{V_H}(1-\frac{\partial\epsilon}{\partial\alpha})$$

Therefore, increasing the wing lift slope decreases the neutral point, as will an increase in downwash. Increasing the tail lift slope has the opposite effect.

So there is no blanket statement.