Eek, something squashed my potato plant! Will the potatoes survive?

[Hopefully]

I think that a cat jumped off the flat roof next to my potato plants (in a bag, on the patio) and has broken about 60% of the stems. Will the potatoes be OK in the ground? We're going away for a week from the 26th, so I'm debating whether to dig them up before we go (they'll probably be fairly tiny, but they went in quite early so might be OK) or leave them in the ground - will they start to rot if the plant above has been brutally murdered?

I would not worry too much. The heavy rain can batter potato tops down. The stems that are broken may stand up again and there are some not broken that are still feedng the potatoes undergrond. Even if the plant is dying the potatoes underground will not go rotten by the end of the month.

The other potato thread last night had advice on lifting and storage.