The childbirth might not be unexpected, but the need to take time off would be. The op can credibly claim he did not intend to take anytime off at all and it is only because wife needs him and this was unexpected.
I think you're setting a precedence that it is you vs company. If you're upfront and they work around this or even embrace it, you know they are a good company to work with.
"Whoops, turns out my wife was pregnant for the past nine months, who knew?"