It is unlikely that the Italian Cypress will grow anything on the bottom 2' of trunk as you are describing. Once the limbs are removed from the trunk, it is rare that any foliage will grow back. The Italian Cypress commonly sold is a cultivar of the species that has strong fastigate tendencies. In other words the limbs grow straight up to give it the typical look that it has.
Incidentally 2' apart is way too close to plant these trees and have them do well. This is particularly true in arid areas. 12' - 24' depending on the rainfall of your area, is more realistic.
A different tree should have been used for foliage all the way to the ground, or perhaps as you say, fill in with bushes/etc.

I have about 34 of them planted a foot or two apart. I think they are about 30 years old and grew over 40 feet. I just topped them as they were too overwhelming at that height. Once you lose the green parts, they don't grow back. You have to wait for new growth. So the bottom of your trees may not have any growth...

Plant low shrubs in front of the cypress to hide the missing limbs. Rosemary and pacific blue juniper are good choices.