If both the curb and the sidewalk in front of my property are damaged,
will they be replaced at the same time? 

Generally, no.  Because the repair work generally involves root pruning of a mature tree
on either side of the tree, and trees will not survive if roots on both sides are removed, the
sidewalk is generally replaced first.  After the tree has recovered from the root pruning
on the sidewalk side, which can take up to five years, the roots are then pruned on the curb
side and the damaged curb is replaced.