You do NOT want to ride the MRT/levee all the way from Baton Rouge to New Orleans - nor the River Road either. Because of the meandering route the river takes, you add 30-60 miles needlessly and gain nothing (I-10 mileage 64, Hwy 61 mileage - 66, River Road - 90-120 depending on shortcuts). Dropping onto/riding River Road for any distance is taking your life in your hands due to traffic, road condition (extremely poorly maintained and seashell strewn), and the fact that speed limits are not honored. The MRT/levee bikepath near Baton Rouge is incomplete, short and doesn't end up getting you out of the BR metropolitan area.
As far as riding the MRT from Norco to New Orleans goes, I wouldn't do it. The bikepath between Norco and Kenner is not well-maintained - you are riding on grass for significant stretches rather than pavement. There are too few convenience stores that could be used as bailout points/refreshment points for water. Heat/humidity being major concerns in Louisiana EVERY summer, this is/should be a major survival consideration (this morning it was 80F/80% humidity at 7am... the temp rose to 91 by 11am). Also, the Norco area is an industrial/oil refinery wasteland - it literally stinks. You can get through the stench fastest on Hwy 61. This is something that Google Maps will never tell you.
Approaching New Orleans, the MRT/levee bikepath from the airport going East is recommended due to its lack of traffic, condition and patroling by the Levee Board Police (in case of medical emergency/accident). They are nothing but supportive of cyclists. The only real drawback to the levee bikepath is a total lack of shade.