For Madhya Pradesh:
"Surveys carried out by NFHS 3 recorded high prevalence (over 60%) of malnutrition among children under six in MP" - from a Government source (page 28) :
http://wcd.nic.in/icds/apip/APIP 2012- 13 _Final (MP).pdf
Also check this:
Madhya Pradesh | UNICEF
It helps to some extent, and that help matters to a poor kid.
Besides, the core issue is why non-vegetarians should be deprived of egg, vegetarians can choose not to eat it.
Please read the article, nobody is forcing vegetarians to eat egg.