If he is listed in your room for the whole week, then you'd have to pay for the
DDP for him for the whole week. If he is not listed in your room then no, you would not be able to use a dining credit to pay for his meal. Disney is now very strict on this. Waiters are not allowed to let you order more meals than the number of people showing up on your room key. If your room key shows 1A 2C, then all the waiter is allowed to let you order is one adult meal and two kids meals.
This is what the WDW DDP broshure says under FAQ:
Q. Can I use my
Disney Dining Plan to redeem meals for friends or family members who
are not included in my reservation or have not purchased a Disney dining plan?
A. Sorry, you may not use your Disney Dining Plan to redeem meals for friends or family
members who are not included in your reservation or have not purchased a Disney
dining plan.
Sort of along the same line: last Feb my husband and I took our grandson to WDW on the DxDDP. Our last couple of days we realized we were going to have credits left over (due to skipping some ADRs we had scheduled), so asked to order an adult meal for him. Even though he was listed in the room with us and we had paid for his DxDDP, every single restaurant refused, saying we were only allowed to order exactly what was on our room key which was 2A 1C. Even when we told them we were just trying to use up extra credits and they could see we would be leaving the next day, they still wouldn't let us order anything other than 2 adult meals and 1 kids meal that was on the room key. We even tried to get an adult meal to go, to eat later and was denied at every single TS. Now our last day the CS at our resort did allow us to use up four adult meals and two kids meals to go to the airport, but only after a manager looked at it and verified that we were checking out that day and needed to use up the credits, but not a single TS restaurant would allow us to order an extra adult meal. Knowing the rules, I didn't really expect them to, but thought since those credits would be going to waste and it was the last two days of the trip, thought it might be worth a try.