  We study Bose gases in $d$ dimensions, $d \ge 2$, with short-range repulsive
pair interactions, at positive temperature, in the canonical ensemble and in
the thermodynamic limit. We assume the presence of hard Poissonian obstacles
and focus on the non-percolation regime. For sufficiently strong interparticle
interactions, we show that almost surely there cannot be Bose--Einstein
condensation into a sufficiently localized, normalized one-particle state. The
results apply to the eigenstates of the underlying one-particle Hamiltonian.
