Is it possible to have accumulation of electron density in the inter-nuclear region even if the overlap integral is zero?
If you define overlap as given by the overlap integral, 

$
S_{ij} = \langle \psi_{i} | \psi_{j} \rangle
$

than you can have an accumulation of electron density in a specific part in space even though $S_{ij} = 0$.

Of course, if the complete wave functions of the two AOs are completely non-overlapping in all space, for instance because the centers of the two AOs are seperated by a long distance (say more than 5 A), then there can be no accumulation of electron density anywhere. This is of course logical. There is hardly any accumulation of electron density between two atoms that are quite far apart.

An interesting scenario exists where two wave functions have opposite sign and an overlap of these wave functions actually gives a decrease of electron density. This is termed deconstructive interference opposite to constructive interference when there is an accumulation of electron density.