Dear Chris,
C^T embeds in [(C_T)^op,Set]; i.e. any category of algebras embeds in the presheaf category of the Kleisli category.
This part is morally clear, I think, via the notion of density. A functor F: A --> B is called dense if the induced functor Hom(F, -): B --> [A^op, Set] is full and faithful. An equivalent condition (stated loosely) is that every object of B is a colimit of objects of the form F(a) (with a in A) in a canonical way. (See e.g. Categories for the Working Mathematician.) Now take a monad T on a category C. Every T-algebra is canonically a coequalizer of free T-algebras. So every object of C^T is canonically a colimit of objects of the subcategory C_T. As long as "canonically" means what I assume it does (and I haven't checked the details), this tells us that the inclusion C_T --> C^T is dense. Hence the induced functor C^T ---> [(C_T)^op, Set] is full and faithful - which I guess is what you mean by an embedding. All the best, Tom [For admin and other information see: http://www.mta.ca/~cat-dist/ ]