I think there are two opposing effects that might happen if you try something like this.

1. People get less defensive about the identity politics of the debate, which opens both sides to actually engaging with the other side, not automatically rejecting the other side, treating arguments less like soldiers, etc.

2. People are more likely to let statements they disagree with slide, and the depth and vigor of the discussion is reduced, by focusing on agreements and amicability, rather than disagreements.

A lot of other factors are at play here, but depending on what your biggest problems are in debate, and how much this sort of change will affect them, it might still be a good idea. If the debate is already an actual debate and argument, rather than political attacks and rhetoric, then changing the context to something like this would probably be counterproductive. If the debate is political attacks and rhetoric, on the other hand, a little bit of humanity and amicability is probably not a bad idea.