I once asked a similar question on some online forum [1] where many linguists hung out. My question was if an English-only speaking household left a general interest Spanish language TV station on most of the time when they weren't actively using the TV to watch something, so that their child received a very large exposure to Spanish language programming (news, sports, soap operas, sitcoms, movies, etc) from birth onward, would the child naturally learn Spanish?
I don't recall for sure what the linguists who responded said, but I think they all said the child would not learn Spanish from this.
[1] I have no recollection of where this was.