I examined the results of (integer->char 256), the first Unicode character outside the 8-bit range; (integer->char 65536), the first Unicode character outside the Basic Multilingual Plane; (integer->char 128), the first non-ASCII character; and (integer->char 0), the ASCII NUL character. I then attempted to wrap each character in a string. In all cases where it was possible to create such a string, it correctly had a length of 1.
Full support: Racket, Gauche, Gambit, MIT, Chicken, Scheme48/scsh, Guile, Kawa, Chez, Vicare, Larceny, Ypsilon, Mosh, STklos, KSi, SigScheme, XLisp, BDC, Foment, Owl Lisp, Chibi
Characters 0-65535 only: RScheme, SISC, IronScheme, NexJ, JScheme
Characters 0-255 only: Bigloo, SCM, Shoe, TinyScheme, Scheme 9, S7, UMB, Elk, SXM, Sizzle, Inlab
No integer->char procedure: Rep, Schemik, Llava, FemtoLisp, Dfsch
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 0-65535 only: SISC, IronScheme, NexJ, JScheme
Characters 0-255 only: MIT (but MIT Scheme has UTF8 and "wide" strings, which do support full Unicode), Bigloo, RScheme, SCM, Shoe, TinyScheme, Scheme 9, S7, UMB, Elk, SXM, Sizzle, Inlab
No integer->char procedure: Rep, Schemik, Llava, FemtoLisp, Dfsch
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
This test often succeeds because many Schemes treat anything that is not numeric or a delimiter as an identifier, even if they only understand 8-bit encodings.