Yes, indeed. Sodium ozonide is formed in high percentage by the reaction of sodium hydroxide and ozone.
The reaction of ozone and anhydrous alkali metal hydroxides were studied by I.A. Kazarnovskii which confirmed the formation of red colored products known as ozonides. He proposed the following reaction mechanism:
\begin{align}
\ce{2MOH + O3 &-> 2MOH.O3} \tag{a} \\
\ce{2MOH.O3 +2O3 &-> 2MO3.2HO2 + 2O2} \tag{b} \\
\ce{2HO2 &-> H2O + 1.5O2} \tag{c} \\
\ce{MOH + H2O &-> MOH.H2O} \tag{d} \\ \hline
\ce{3MOH + 4O3 &-> 2MO3 + MOH.H2O +3.5O2} \tag{e} \\
\end{align}
So, a mixture of both ozonide and alkali metal hydroxide hydrate is formed as products with the simultaneous transformation of a large amount of ozone to oxygen.
Some information is also there about the structure and chemical properties of sodium ozonide:
Kazarnovskii et al. investigating the reaction of anhydrous sodium hydroxide powder and ozone-oxygen mixtures at -50 to -60°C, observed that, indeed, the hydroxide acquired an intense yellow color which, when extracted with liquid ammonia, resulted in the formation of a dark red solution. The color fades at r.t. Upon evaporation of the ammonia, crystals were recovered. Analysis of the recovered product showed $\ce{90 wt.\% NaO3}$.
Kazarnovskii further reported that $\ce{NaO3}$ is unstable, and that at room temperature it decomposes.
$$\ce{2NaO3 -> 2NaO2 + O2}$$
They also noted, however, that the ozonization of $\ce{NaOH}$ can be done in room temperature but the $\ce{NaO3}$ obtained from the room temperature reaction is not soluble in liquid ammonia, and the ozonide-hydroxide mixture is quite stable. Subsequent studies have explained the difference in the solubility and stability
characteristics of $\ce{NaO3}$ prepared at room temperature and low temperatures. The reason proposed that $\ce{NaO3}$ can exist in two crystalline forms, one being soluble in liquid ammonia but unstable at room temperature, and the other being insoluble and stable although not confirmed experimentally.
The $\ce{NaO3}$ lattice is tetragonal, with $a = \pu{11.61 Å}$ and $c = \pu{7.66 Å}$. The space group is 14/mmm Its density varies from $\pu{1.56-1.60 g cm-3}$ . The standard heat of formation of $\ce{NaO3}$ is estimated as $\pu{45 kcal/mole}$.