Assuming the system can't cope and the cabin has risen to ambient, then, as long as you can get air into the hole and the outflow of air is less than that going in you must get a px rise.
I'm not saying the px rise would be much, otherwise we wouldn't be in this predicament, just that it should be something higher than ambient at a given point in time if there is ram air into the cabin and assuming no additional changes to the number or size of outflow ports. It may also be that the px rise is localised within an area of the cabin. Have you ever watched the tide flow into a marina, odd swirls and currents all over the place.
The only way to really measure it would be to hole the aircraft and maintain a level and then check the cabin altitude versus actual. Even then there may be position or instrument error, plus you might even need a standard atmosphere day in real terms since your px system is generally controlled/read with ref to 1013. (trying to get my head round that bit, it definitely controls it to 1013 but I don't know if we are open to atmosphere)
If we are talking about a sim (I hope we are) it all really depends on the model the programmer has created.
Just out of interest my fuel tanks are partially px'd by ram air.
If you have ever travelled on the London underground in summer with all the windows open, when you pass an opposite direction train in the tunnel, the px head of the on-coming train forces air in through the windows of your carriage sufficient to pop your ears.
With regard to the 'twice the ROD you suggest' - all I was trying to say was the aircraft I fly has an actual ROD in an emergency descent from 370 of between 7000 and 8500 fpm. So you've surprised me that 777 is so graceful.
Need to sleep now.