Yes and No.
Yes ... open up the save in Civ4, open World Builder and save it as a WB file. Then start a new game with BAT and 'play a scenario' ... scroll down the list of scenarios until you find the WB file you saved above. Note that this is a TOTALLY NEW GAME and resets all things (city production, whip anger, GP count, etc, etc).
No ... BAT is a mod and you can only play saves generated by the mod (this is a Civ4 thing and impacts any mod you play). You can't play a BAT save without BAT. You can't play a mod-less save with BAT.