I examined the result of (integer->char 256), the first Unicode character outside the 8-bit range, and then attempted to create a string containing it. I then tried the same thing with (integer->char 65536), the first Unicode character outside the Basic Multilingual Plane. In all cases where it was possible to create a string, it correctly had a length of 1.
Full support: Racket, Gauche, Gambit, Chicken, Scheme48/scsh, Guile, Kawa, Chez, Vicare, Larceny, Ypsilon, Mosh, STklos, KSi, SigScheme, XLisp, BDC, Foment, Owl Lisp, Chibi
Characters exist but can't be in a string: MIT
Character 256 exists, but can't be in a string; character 65536 does not exist: RScheme
Character 65536 does not exist: SISC, IronScheme, NexJ, JScheme
Character 256 does not exist: Bigloo, SCM, Shoe, TinyScheme, Scheme 9, S7, UMB, Elk, SXM, Sizzle, Inlab
No integer->char procedure: Rep, Schemik, Llava, FemtoLisp, Dfsch
I also tested to see if Schemes could handle character 0 (ASCII NUL) correctly. All Schemes in the test suite treated it like any other character.
I tried to define the identifier π with the value 3.141592653 and then evaluate it.
Successful: Racket, Gauche, Gambit, Chicken, Bigloo, Scheme48/scsh, Guile, Kawa, SISC, SCM, Chez, Vicare, Larceny, Ypsilon, Mosh, IronScheme, NexJ, JScheme, STklos, KSi, SigScheme, Shoe, TinyScheme, RScheme, S7, BDC, UMB, Elk, Llava, Sizzle, FemtoLisp, Dfsch, Inlab, Foment, Owl Lisp, Chibi
Unsuccessful: MIT, Chez (can't enter π at the REPL), Scheme 9, XLisp, Rep, Schemik, SXM