Of course it is. That's how it always works when mad scientist devices go comedically haywire!
On an ordinary day, it could well be a problem. But structurally damaging the shelter would be a top-tier emergency, and with a ton of heavy destabilizing snow and a tower directly on top of them that could be unsettled by an explosion, the force that would be required to dent the shelter's built-tough doors is considered a significant threat. As a result, Acumen won't tolerate attacks on the shelter structure. If you attack the doors (or walls or ceilings) with magic (or other people's canon equivalents thereof, for interested parties) the attack will be harmlessly absorbed. If the attack is powerful enough to be considered a threat to structural integrity, you will probably pass out and wake up again sometime later, power-nerfed, since that would be considered an attack on Acumen's facility.
And, before anyone asks, physical attacks with or without weapons will be similarly futile, and anything strong enough to do structural damage may result in physical nerfing. You're more likely to damage yourselves or other people than the shelter in a lockdown state.
As far as emergency supplies go! There should be some pretty standard emergency kits stashed in various locations in the shelter -- such as under sinks or stowed high up or down low in closets. They won't be located in private rooms, but in public areas. First aid supplies, blankets, flashlights, sealed water bottles, face masks, even some strange items. (For instance: there's a little sphere with a small panel on it that, when pressed, lights up and floats into the air, spins slowly in a circle with a pulsing noise, and then after about fifteen seconds floats back down and turns itself off again.) So on at least this front, the warden has you covered; you'll just have to find the gear yourself, since Acumen does not consider it necessary.