Hi my son is now 31/2 years and NO, they don't eat very much when really ill. I live in England at the moment (from Winter Haven)and you don't get anti-biots for virus, nothing here - you suffer through it with all the stress!
Lots to drink of 50/50 real fruit juice and water, milk diluted as well. Plain simple very small snack plate of the dry cerial, (cherrios does work well for this)bagel, baby type organic biscuits, plain rice cakes... that sort of really bland food non-wholemeal if they have upset tummies. One plate for each of them and see if they take anything after they had some pain relievers. Put the snack asst in ice cube trays with a baby applesauce dip to see if you can tempt dipping.
I knew my son was bad when he refused his absolute favourite of fruity oatmeal. He lost more then 10% of his body weight in a week.
On the upswing - when they start to feel better, be prepared for the voracious eating spree. They cannot get much into their shrunken tummies so my friends and I noticed that they really needed to eat every 30 minutes. I carried little sandwiches, baby snack bars, raisins etc everywhere and had to stop the car on busy roads as he had to have it NOW!!!
Get ready for healthy filling snacking that may last as long as a week, day and even into the night for my girlfriends daughter that had to be seen at hospital it got so dramatic.
Good luck, your email brought back that sunken sick feeling that I remember so well.