In this paper we present an analytical procedure for the computation of the node isolation probability in an ad-hoc network in presence of channel randomness, with applications to shadowing and fading phenomena. Such a probability coincides with the complement of the coverage probability, given that nodes are distributed according to a Poisson point process. These results are used to obtain an estimate of the connectivity features for very dense networks. For the case of superimposed lognormal shadowing and Rayleigh fading, the connectivity improvements achievable by means of diversity schemes are investigated.