As a TA I taught 'informal' music in schools for twenty years, but was not experienced or qualified regarding exams. Our DS played several instruments, eventually Grade 8 saxophone.
Grade 1 is only just the VERY START of learning anything about music, so I can't really imagine why you would consider taking an exam without music!
Two possible scenarios occur to me: ONE - the pupil's mind goes blank, and he is unable to complete the pieces. TWO - freed of having to look at the 'dots' he can put more expression and creativity into the piece; but they are only going to be very simple pieces at Grade 1, and the scope for expression will be limited.
He will, of course, have to do a sight reading test, aural, scales etc.
A Distinction should be perfectly possible for a well prepared, excellent performance, using the printed music.
Sometime, I'd be interested to know why you would consider it 'sans music'!