Possibly not, but then you can't please everyone.
As for what type of critique to ask for - the majority of moved posts don't even ask for a critique at all. If someone shoves a picture in there and just says 'what do you think?' - well, they will get just as good a response in the general or landscape galleries so that's where it goes.
The Crit is really for people that have a problem, either with an image or their photography in general. If people want board members to give up some of their time and use their knowledge and experience to help solve the problem then I don't think it is too much to ask to expect the poster to put in some effort and meet them half-way.
I don't think it beyond the capabilities of anyone to try to express in some way what it is about the picture that is bothering them. There are really only two broad areas that usually cause someone a problem - technical (exposure/contrast/colouDoF etc) and framing/composition.
I've taught Photography in Colleges for over 15 years and in my experience when someone comes up, shows you a picture and says 'what do you think' what they really mean is 'I took this and I think it's dead good and I want you to agree with me'. Similarly, when people have a genuine problem they make the best attempt they can at trying to put their doubts or worries into words. It's quite easy to distinguish between the two.
I used to send people a PM whenever I moved a post, explaining why it was moved and telling them what they should have done, but I only do it sometimes now. Only 1 person in 30 or so ever responded - which would indicate that they were not bothered about getting a crit or not, and I felt that vindicated the move.