Yup. I started guitar at age 9 and even then I had to stretch my fingers still and it challenged my fine motor (which is normal) but I progressed quickly. I don't think anyone's hands are ready at 2.7 (regardless of fine motor ability... we're talking size and strength here... not to mention sensitivity to the strings - ouch! Even with nylon strings you still develop thicker skin on your finger tips and I think the initial discomfort would put a toddler off, no matter how interested).
His hands are too small for guitar at this point, and it seems rather young to start formal lessons. You could buy the family a ukulele to play with (much smaller), and a method book.
