Unfortunately, I don't think there is a way to detect when the Play Store attempts to update your app, unless you have a second app to listen for this event. And even if you have a way to detect this, I don't think you can cancel the update.
Maybe it would be an idea for you to transfer the work you are doing to your second app while the first one is being updated. However, I needn't say that this sounds like a very hacky solution.
You should focus on saving your state and continuing from where you left after the application is updated and started.