When you do the dungeons doesn't neccesarily affect your ability to max social links. But the fewer amount of days you spend going through a dungeon, the more free time you will have left over to focus on things such as Social Links.
But when you do a dungeon can affect Social Link maxing in one way. I chose to enter the first dungeon on a Sunday, because on that day I couldn't do any more social links, as I didn't have the stat requierment to do the only one available at the time.

That said, to have a better chance at going through a dungeon in a fewer amount of attempts, its wise to prepare before going in, by buying new gear, SP regeneration items, lockpicks, etc.

So to have the best possible chance for max social links, do you do dungeons as quick s possible, or delay them? Can't remember how P4 worked in that regard.