  It has been long recognised that, besides being a formidable experiment to
observe the primordial CMB anisotropies, Planck will also have the capability
to detect galaxy clusters via their SZ imprint. In this paper constraints on
cosmological parameters derivable from the Planck cluster candidate sample are
examined for the first time as a function of cluster sample selection and
purity obtained from realistic simulations of the microwave sky at the Planck
observing frequency bands, observation process modelling and a cluster
extraction pipeline. In particular, we employ a multi-frequency matched
filtering (MFMF) method to recover clusters from mock simulations of Planck
observations. Obtainable cosmological constraints under realistic assumptions
of priors and knowledge about cluster redshifts are discussed. Just relying on
cluster redshift abundances without making use of recovered cluster fluxes, it
is shown that from the Planck cluster catalogue cosmological constraints
comparable to the ones derived from recent primordial CMB power spectrum
measurements can be achieved. For example, for a concordance $\Lambda$CDM model
and a redshift binning of $\Delta z = 0.1$, the $1\sigma$ uncertainties on the
values of $\Omega_m$ and $\sigma_8$ are $\Delta \Omega_m \approx 0.031$ and
$\Delta \sigma_8 \approx 0.014$ respectively. Furthermore, we find that the
constraint of the matter density depends strongly on the prior which can be
imposed on the Hubble parameter by other observational means.
