depends on the hole
If you're getting any ram air then the cabin will effectively lead the actual alt or if there is a (i could be wrong here) linear flow over the hole air will be sucked out so cabin should lag the actual alt.
To be honest, I don't think the update rate in the sensors/ processors will keep up. Certainly in the sim I use (not 777) the aircraft reaches FL100 long before the cabin indications. Having said that my ROD is upto twice what you suggest.
My aircraft px system is incapable of showing cabin rates in excess of 2000fpm, just a nice amber dash---sorry cant help more.