Yes with the big maps strat target like the radar factory have an impact on gameplay.
It directly relates to the ability of the field radar to come back up, meaning it stays down longer.
On the large maps you will see "zones" each zone has a city strat. The city needs to be reduced to below 50% ( i think) in order for your strats to make a difference.
So basically in order to play the strat game the first step is to reduce the city below 50% then attack the other strat targets, ammo, troops, radar, fuel etc etc etc..
Resupply by C-47's and M-3's can help to bring the strats up faster then the indicated downtime.
This is my understanding of how strats work anyways but im sure someone more knoweldgeable than myself will come along and fill in any blanks or mistakes I may have made.