In general, they will make every effort to present both the parade and concert unless the conditions are too dangerous to proceed. They'll make necessary changes for the safety of the performers, such as having the stilt walkers off their stilts, but they'll do their best to present both the parade and the concert.
Fortunately, the typical late winter/spring weather patterns in Central Florida are such that the Mardi Gras activities are rarely impacted by rain/electrical storms.