Missions have start date and end date.
By completing objectives you will gain crosses.
Time is going regardless you completed mission or not like in real life.
And as far I know for built in missions (don't know how crosses replacing works for user added missions...?):
It has no impact on campaign - no effects,

Crosses you can replace for some additional bonus missions etc. on ubi web site?
It would be nice to see some effects of our efforts in campaign!
But what effects it could be?