I guess it would depend on the reasons for not coping and the best solution to them.
If I had MH issues that were causing the problems, I would be cautious, yes. But - how much of the paranoia or worries about, say, the children being taken away is warranted and how much of it is down to the underlying issues?
With DD, we've been quite frank about how much of a handful she is, and I said to our GP recently that there were times that I didn't think we'd make it through (as a family) intact.
However, we have the "cushion" of knowing our GP socially (as well as one of his colleagues at the practice), and of having an older DS with whom we just clicked. So they know the "real" us, as it were, not the stressed us. Also, DD has been in nursery part-time since the age of eight months, and I feel this is another layer of protection against any damning/erroneous SW conclusions.
I am trying really hard to address your questions. In short, I wouldn't be too happy about saying I wasn't coping, but part of that would be the fact that I wasn't coping (IYSWIM).
Tough one - I hope this is a good answer.