I was hospitalized several days when my baby was only 6 months. I had my baby brought to the hospital so that I could nurse him during the day, and he was given bottles of expressed milk at night (not really necessary for a toddler though). Toddler nursing is obviously much different, but if you have him come to the hospital and offer to nurse using the day I would bet he would do just fine. Whomever he stays with may just need to be prepared to snuggle with him awhile to get him back to sleep if he wakes. It is very possible, however, that the night nursing may decrease some once all of his teeth are in.
I think a bigger concern is that most moms lose their milk during pregnancy, and he may wean due to that.
K. Sophia - Mama to my little lactivore, the amazing Mr. X (11/10).