ConEmu do not do any magic with your console application output. Actually, it just shows the contents of the Windows' real console.
However, Windows console supports unicode from WinNT and it's not a problem to use any unicode characters if they exist in the font used to draw console contents: http://conemu.github.io/en/UnicodeSupport.html
However, current cygwin versions and msys v1 are using ANSI for console printouts which leads to limitation of the available character set. AFAIK msys v2 uses unicode and it might act better with UTF-8 glyphs.