Condolences on the loss of your chick.

I'm afraid I missed your question about Nutri-Drench and Corid, so I'll provide an answer in case it's helpful to someone in the future.
The short answer is no, Nutri-Drench should not be offered while treating with Corid. The reason is that amprolium, the active ingredient in Corid, works by blocking thiamine uptake (it's a thiamine uptake inhibitor) in the coccidia protozoa; Nutri-Drench contains thiamine, so it would be counterproductive to administer both at the same time. This
post has a discussion on the topic.