Including the system databases along with user databases for db integrity checks and building of reindexes

We have a maintenance plans which checks for the database integrity and rebuilding of indexes
of all user databases excluding the system databases of master, model, and msdb. Since the system
databases are having metadata about other databases is there any problem in including the
above databases along with the other user databases in the maintenance plans for integrity
checks and rebuilding of indexes? Also while building the indexes what are the overheads in time
if we are keeping the indexes online or is there any advantage in keeping the indexes not in online while rebuilding the indexes?