Sleeping SPID with Open Transcations
I am not sure if your case is similar, but you can see similar behavior with Distribution Agent SPIDs on subscriber.  

When its not applying any changes it looks something similar.



So in this case its normal behavior.

Hundreds of idle sessions, as you can imagine, would not impact CPU.  But those sessions might be waking up and doing things. The real question is where are those spids coming from? Are all of them from the same application? If so, it might be time to ask the application support guys why it has so many connections hanging around. Maybe they are not closing connections properly.