Firstly, it's not an IC, but a single transistor. IC stands for integrated circuit, which contains more than one transistor or component on the same chip.
To answer your questions, yes this circuit will damage the transistor, which is not designed to work in this mode, hence no mention of the breakdown voltage on the datasheets. What you'll more often see is a maximum reverse voltage rating for the base-emitter junction, but this will be significantly lower, than the breakdown voltage, to ensure the component can tolerate it, without damage.
The circuit won't work with a zener diode, at least not very well, because they don't exhibit such an extreme drop in resistance, as the voltage increases and a sharp increase in resistance, as the current reduces. A zener diode tends to sit there, maintaining a constant voltage. You might be able to get some oscillation from higher voltage zener diodes, as they have more of an avalanche effect, but I doubt it'll be significant. I suggest trying it.