In the EXALT Covert Data Recovery missions, what's the effect of disrupting comm relays?

Disabling comm relays only disables the primary weapons of all EXALT operatives on the map. They will need to spend at least the second part of a turn reloading to fire again, but they may choose to use that half-turn to move, use a grenade or an ability instead (though they will have to reload eventually in order to fire).

Disabling those relays has no effect beyond that, the number of enemies that will enter the map will be the same and their weapons will not be affected.

It may reduce the size of the next waves; I'm honestly not sure.

It does however force every active EXALT unit on the field to spend a turn 'reloading' much as if you hit them with a disable weapon sniper shot.