This is surprisingly feasible. In a recent paper about alien civilizations building Dyson-rings around pulsars Zaza Osmanov found their habitable range "should be of the order of (10^−4 to 10^−1) AU with temperature interval (300–600) K for relatively slowly rotating pulsars and (10–350) AU with temperature interval (300–700) K for rapidly spinning neutron stars, respectively." Obviously, for the temperature range specified. So, thermal habitability is fine for the parameters of the secondary star and its planets even for rapidly rotating pulsars.
Provided the secondary star wasn't in the plane of the emitted radiation and, therefore, subject to the pulsar's pulsing it should be safe in terms of radiation.
Since a habitable planet needs a strong geomagnetic field to protect its biosphere from radiation, if the pulsar beam glanced off the planet's magnetic field this produce the most magnificent auroras in the galaxy.
Any life evolving on the planets of the secondary star will be adapted for higher levels of radiation than those of most other planets. Somewhat more extremophile, but definitely more radiation adapted.
Essentially its not implausible that a habitable planet could in the secondary star's planetary system. The odds against it being a safe place to live long term are high. However, if the conditions are right, then it is possible. This means the distance is great enough and its position relative to the pulsar is out of the path of its radiation beam.