Depends mostly on temperature. For simplicty let's assume the room has a volume of $20m^3$ so we have $10m^3$ of dry ice at, say -80°C, and $10m^3$ of air at 25°C. That's about 16000 kg of dry ice and 12kg of air. Once you connect the two, the air will simply cool down rapidly to -80°C. Given the massive difference in mass the final temperature will be very close to -80°C and there will only be a very slight rise in pressure. If you are temperature protected you will be fine.
Now if you apply external heat (or have poorly insulated walls), the temperature will start to rise. As the ice goes above -78°C the dry ices will start to sublimate and the pressure will rise. That also increases the sublimation point. When you hit about -56°C ther pressure will be 500kPa pressure. At this point liquid $CO_2$ becomes possible and the ice will start to melt. 500 kPa is the same pressure you would experience at a water depth of 40m, so with proper gear and training this is entirely survivable.
If you finally reach room temperature, the liquid $CO_2$ will boil and you'll end up just shy of the region where $CO_2$ becomes Supercritical carbon dioxide. Final pressure will around 7MPa and you'll have a mixture of liquid and gaseous $CO_2$, with the majority still being liquid. That pressure correponds to a water depth 700m which is just about at the hairy edge of what humans can do provided enough training, gear and process and only for very short time periods.