The OP asked if he would gain any benefit from training in a reduced state. He said that he knew it would be safe.
I don't see any reason not to take him at his word on that. 'Sick' can mean a lot of things.
Yes, you can gain a lot of benefit from it. Relying on your lizard brain for fine motor skills is not an easy skill to develop but I think it's an important one. When we start dry-fire practice we are typically at a low skill set. As our skill set develops, falling out of the habit of dry-fire practice is pretty common, because it's boring, time consuming, and you don't see the improvement you did when you started.
At this point I exclusively dry-fire practice while doing maintenance exercise (core, cardio, etc.). I do that because otherwise there just aren't enough hours in the day to get it done. Same reason I brush my teeth while I shower. It's an annoying maintenance thing that just needs to get done or you'll fall off.
When I started it was difficult to get my reps in proper because my body was gasping for air or in pain. After awhile the reps started to come natural again because I could do it without all my faculties focusing on the fine motor skills. I think practice while sick is pretty equivalent to practice fatigued.
If you can stand up you can practice, and safely. How you personally recover best from illness is what should determine what choice you make.