The two other answers addressed the similarity between the SAR and rarefaction. I wanted to address your second question:
%%Also, does METE apply to other forms of macroecological patterns, ie to the accumulation of species in different communities?%%
METE does predict more macroecological patterns than just the SAR, including the species-abundance distribution, community and species-level body-size abundance distributions, and distance-decay patterns (see Harte 2011 for a more complete list). As Leonardo pointed out, METE's predictions are invariant with respect to community type and only take the information on the measured constraints into consideration when making a prediction.
It is currently less clear if METE applies across community types or biomes. Harte (2011) suggests that METE should primarily apply within communities or biomes, and that failures of METE may be due to the fact that that samples capture too much environmental heterogeneity. That being said one can never truly define a completely homogeneous ecological sample or community (Palmer and White 1994), and the datasets we examined in the current study contain environmental variation and spatial species turnover at all scales yet METE still yielded accurate SAR predictions. Therefore, if we view METE as a practical tool for predicting the scaling of diversity from local to regional scales then we may not need to worry too much if our study sites where we are applying the inferences contain only one community type. Continental scales pose a special set of problems for predicting the scaling pattern of diversity because of species range restrictions (Allen and White 2003). Future iterations of METE may attempt to solve these problems though.
Allen, A. P., and E. P. White. 2003. Effects of range size on species-area relationships. Evolutionary Ecology Research 5:493–499.
Harte, J. 2011. Maximum Entropy and Ecology: A Theory of Abundance, Distribution, and Energetics. Oxford University Press Inc., New York.
Palmer, M. W., and P. S. White. 1994. On the existence of ecological communities. Journal of Vegetation Science 5:279–282.