If it does track across half the Gulf, or all of the Gulf, it would have time if conditions improved. I'm not sure if shear is especially harmful in this situation given the direction it is coming from.
SHIPS intensity text output for 92L at the bottom of this directory: ftp://ftp.nhc.noaa.gov/atcf/stext/ For reference for the 0Z run on the 12th (8pm on 11th) SHIPS was using the BAMM model, medium layer, which takes it into central Louisiana, so if it were to continue west conditions could be different of course than the track SHIPS was run from.