Comma after "and that"

Solution 1:

I read it as a parenthetical element. 'if he did' could be removed from the sentence without changing the meaning. Some examples should make this clear (taken from http://grammartips.homestead.com/interrupters.html):

Take, for example, the way Linda responded to being accused of
bias.

That explanation, as I have already said, doesn't really hold water.

You should, nevertheless, continue your efforts despite this recent disappointment.

He cannot, however, hope to defeat a popular incumbent.

The italicised parts are parenthetical elements. They could be removed from the sentence and it would still read correctly.