What will happen if I drink baby oil? Will it work as a laxative?

Wouldn't chance it! Uncertain--i can find no exact references in pubmed re: ingestion of baby oil. Nevertheless, there are well characterized syndromes associated with aspiration of toxic oils with resulting pneumonitis, as well as in the 1990's an eosinophilia-myalgia syndrome associated with toxic-oil intake, diffuse fasciitis, & eosinophilia. Don't take a chance! still in doubt, call the poison control center.
Agree w/Dr Cattano. I am not sure I understand why you wouldn't want to simply ingest something specifically made as a laxative for human consumption as opposed to trying something that would be considered entirely unorthodox. Do you have any other unusual types of cravings for food or beverage that most other people would find unusual?