If the conditions improve, you can either carry it or throw it away. If you want to sit or lay or down before the start it will keep you warm and dry. Put band-aids over your nipples. Depending on the tops you wear, most runners get alternately cold and wet. The shirt can rub against your nipples and cause great discomfort not only during the race but also for several days after.
Several companies make small round patch types that work very well.
Try them out on long runs before the marathon. It is very handy to take an old set of sweats to wear around before the race and then discard them. I don't mind looking for the sweat truck after a 5 or 10 K race, but after the marathon it's not fun. Any additional clothes taken to the start get left at the start. Puddles Watch out for puddles along the way.