If during the flooding you got water coming up out of the floor drains and removing the down spouts from their pipping caused a change, that would indicate that your floor drains are piped to daylight. It would also indicate the floor drains are also tied to the gutter down spout drainage. That is not a good idea. Unfortunately removing the down spouts from the system means that unless you took some other action, all of the rain water from your roof is going into the ground around you house which is not a good thing.
If this is the situation I would agree with blocking you floor drains. They provide no advantage during a flooding situation. Unfortunately during a situation such as a bursted water pipe or flooding due to a plumbing problem or water coming in around the foundation or footers they will not be there either.
Floor drains provide no benefit,with respect to hydrostatic water under the basement floor.