Our 737 FCOM says the following about rolling take off or not:
A rolling takeoff procedure is recommended for setting takeoff thrust. It expedites takeoff and reduces risk of foreign object damage or engine surge/stall due to a tailwind or crosswind.
Our performance software has as standard an option activated that calculates an increased line up allowance of roughly 100 to 120m.
Take off thrust before being aligned, especially out of a 90° line up can lead to very nasty results. However when lining up out of a rapid exit way it can be possible.