It depends on what type of stress and over what period of time you are talking about. I had a period in hospital in 1999 with nervous exhaustion, this was mentioned in our application. Also your doctor has to do a report so can explain in more detail than just simply "Stress".
I know from my perspective once I knew what it was, I no longer put myself in these sorts of situations and have learnt from it. If it were a serial thing and a regular part of your life then they would look at the effect this may have on the children.
My DH was signed off from work for stress for a short period. It's had no effect on our adoption. I think Karen is right and it depends what type of stress it is, whether it is an ongoing thing that could affect the children in the future.