If the child bathes with sufficient regularity he probably smells fine, and in my opinion body sprays, especially cheap ones, smell pretty awful anyway so I certainly wouldn't think someone using them smelled any better than they did normally.
Unless it is very subtle, body spray of any sort strikes me as weird and tacky.
It usually smells fake & overpowering, and it often aggravates other people's allergies or sensitivities.
I understand using a small amount of quality perfume or cologne for a formal event, but for everyday it seems unnecessary to have a signature scent -- especially for a toddler.