If you got enough liquid in there, yes, but I think it's really unlikely you'd get that far. Until you've cooled things down, the liquid you put in is going to boil off, which has a corresponding volume expansion of almost three orders of magnitude. Without good ventilation (which you're not going to get if you're not cutting into the box because of the contact switches) this is going to lead to an explosive pressure buildup in the box, which seems like a really bad idea under the circumstances. There are lots of other possible ways for it to go wrong, e.g. the wires could break under thermal stress, which might lead to bad things; the boiloff could disturb the pendulum in the tilt sensor; etc.
