Kleinberg-consistency of spectral clustering
Answering my own question, with a hat tip to Misha Belkin (private correspondence). It is easy to see that the unnormalized mincut and the RatioCut algorithm (see here for precise definitions
http://www.kyb.mpg.de/fileadmin/user_upload/files/publications/attachments/Luxburg07_tutorial_4488%5b0%5d.pdf
) are Kleinberg-consistent. This is because the intra-cluster distances/similarity does not influence the objective function in any way.

The Ncut-based clustering algorithm, however, is not Kleinberg-consistent. This can be seen by making the similarity weights within some cluster sufficiently large that it is able to absorb nearby clusters with negligible extra charge.