I agree with @JLeslie and with the others here. However, studies on the subject are being conducted all the time – with new infomation giving us glimpses into how the brain works with regards to communication, especially with babies and toddlers.
This article reminds us that language is not isolated but rather a part of communication – something we often forget when trying to learn a second language – at any age – and why adults find it so difficult and frustrating to pick up a new language – by learning an hour a week. I have a lot of experience with this.
Babies, until the age of 9 months, should be exposed to more than one language – this will help them later on in life – and not only with languages and linguistics – but also with how they approach problem solving.
Two- and 3-year-olds are not only increasing their vocabularies, they’re starting to recognize the speech patterns they’ve been hearing since birth. The earlier you introduce a second language, the easier it will be for your child to pick up its unique sounds. The ability to hear different phonetic pronunciations is sharpest before age 3, and we lose the capacity to hear and produce certain sounds if we aren’t exposed to them early on. So just hearing a television show, listening to music, or learning a few words in a second language will give your child essential tools for appreciating it now and learning to speak it later.
I say go for it – but for the right reasons. Don’t expect a conversation in the chosen language after a two year old has been studying for a year, one hour a week.