The recently identified source class of pulsar haloes may be numerous and bright enough in the TeV range to constitute a large fraction of the sources that will be observed with the Cherenkov Telescope Array (CTA). In this work, we quantify the prospects for detecting and characterizing pulsar haloes in observations of the projected Galactic Plane Survey (GPS), using a simple phenomenological diffusion model for individual pulsar haloes and their population in the Milky Way. Our ability to uncover pulsar haloes and constrain their main physical parameters in the CTA GPS is assessed in the framework of a full spatial-spectral likelihood analysis of simulated survey observations, using the most recent estimates for the instrument response function and prototypes for the science tools. For a model setup representative of the halo around Geminga, we find that about three hundred objects could give rise to detectable emission in the GPS survey. Yet, only a third of them could be identified through their energy-dependent morphology, and only one-tenth of them would allow the derivation of strong constraints on key physical parameters like the magnitude or extent of suppressed diffusion around the pulsar. We also provide a list of known pulsars that could be hosting a detectable (Geminga-like) halo in the GPS and assess the robustness of our findings against several systematic uncertainties.