There is no empirical evidence to suggest that reading Nursery Rhymes or singing will add to the learning curve, or give any child a headstart.
The idea behind singing or reading is really to orient children with listening skills, and even songs or stories are replaced by everyday conversation, it aids the learning process. The intent as mentioned communicating with the child, and getting the children's mind tuned to listening different sounds that eventually become words that they utter. Music, Rhymes etc are therefore a simpler way for parents to communicate!
It is a form of relaxation, a form of recreation and music is great therapy in any case.
My recommendation is to have conversations.... and some may involve a short rhyme.