Just my humble opinion. for what it's worth.
I think, at least unconsciously, you already know the answer to your own question by your use of the word 'interrupted' and by your use of the modifier 'horribly' in 'horribly wrong'. This suggests to me that you know that it would be 'wrong' but are just not quite sure of the degree of wrongness!
What justification can there be for 'interrupting' a performance of a piece of music?
Great music deserves to be played and heard, by the audience, as the composer wrote it and intended it to be listened to.
If I were a member of the audience at a performance of any kind of music, but especially of classical music, I would be extremely annoyed to have part of the performance 'interrupted' like this.
If indeed the two pieces are related, by all means play them both, but consecutively - the Beethoven first, as a prelude to the Bach, after telling the audience about the connection. If you have a programme, include a note to this effect in there too.
MK