Depends what you call poorly nourished !
Here is what milk banks say :
Donor health and lifestyle
If you are interested in becoming a donor, please contact your local milk bank. Staff there will be happy to answer any questions you may have.
The milk bank will need to know that you are in generally good health and that your baby is under 6 months of age when you start donating. You may continue to donate when your baby is older than this.
Some of the questions that you may be asked are:
Do you have any medical condition?
Do you routinely take any medicines including herbal remedies?
Answering yes to these questions does not mean that you cannot be a donor, but the milk bank staff may want to talk further to you.
Do you smoke or use illegal drugs?*
Do you routinely drink more than 2 units of alcohol per day or 3 cups of caffeinated coffee or other caffeine-containing drinks per day?*
Have you tested positive for HIV 1 or 2, Hepatitis B or C, HTLV l or ll or syphilis?*
The milk bank will arrange for a sample of blood to be taken and tested for infections, which might be passed on through your milk.
*If you answer yes to any of these questions the milk bank will not be able to accept your milk.