A recent study by Verbunt et al. (2017) models the pulsar speed distribution as the sum of two Maxwellians, one with a sigma of $\sim 80$ km/s and the other with a sigma of $\sim 330$ km/s. About 30% of the population are in the low speed Maxwellian. A plot of the (model) distribution is shown in Fig.9 of that paper.
The figures quoted above are for young pulsars. This is important for your question because older neutron stars might form a biased population where they have undergone significant acceleration and/or the most rapid ones have already escaped (and indeed the model distribution for all pulsars shows fewer fast-moving objects as a fraction of the whole).
To answer your question though is non-trivial and probably requires an accurate model of the Galactic potential. A starting point would be to assume that the observed population originates in the Galactic plane (since they originate from young, massive stars) and that the observed velocity distribution represents the natal distribution. The Galactic escape speed is probably a function of Galactocentric radius. Piffl et al. (2018) estimate a local escape speed of $537^{+59}_{-43}$ km/s, increasing to $>600$ km/s at Galactocentric radii $<4 $kpc and decreasing to about 500 km/s at Galactocentric radii $>11$ kpc. This variation is perhaps small enough that we could take a value of 550 km/s as typical for the necessary escape speed in the pulsar sample. In which case, I would estimate the fraction of young pulsars that will escape to be $\sim 25$%, though you could presumably use Verbunt's model parameters to get a more precise (though not necessarily more accurate) result.
