Since safes will vary greatly based on build quality (and price) and mesh factors will play such a big role in the final determination, I would say that the best way to know for sure would be to try it out with one of the sensors you already have. I love the Iris sensors and I've found that have a pretty decent signal strength.
One thing you also might want to consider is using one of the sensors that allows for external contacts, like the Monoprice sensor.
This would allow you to wire a reed switch inside of the safe and then mount the radio part outside. Most safe's will have a hole in the exterior wall for securing to the wall or floor. You could run the wire through one of those. Obviously that still leaves it vulnerable to being disabled but it does allow you to hide it rather than have it right there in front of you attached to the door.
