Yes it does. The UTF-8/16/32 encodings are defined in the Unicode standard (chapter 3.9, page 89), they're not some kind of aftermarket add-on.
"UTF-8 has the possibility of having encoding errors, where things like UTF-32 do not."
Also not true. The set of valid Unicode code points is the same regardless of the encoding (0-0xd7ff and 0xe000-0x10ffff); anything outside those two ranges is just as invalid in UTF-32 as its UTF-8 encoded equivalent would be. A stream containing nothing but 0xff bytes, for example, would be illegal regardless of which UTF you tried to interpret it as.