As pBAD vector bears AmpR gene, it is compatible for selection in CodonPlus strain which has to be cultured in Cam containing media to maintain the plasmid coding for tRNAs.
yes, you can use pBAD vectors with BL21 codon plus strain (I am not aware of strains that are incompatible with those vectors). As Dominique suggested, just double check that the antibiotic for selection is different from Chloramphenicol.