No? They produce alcohol and CO2 during rising/proofing, and that gas has nowhere to go: it's trapped in the dough. Once heated, that trapped gas then expands during baking. The yeast dies, yes, but bread doesn't rise "because of the death throes of [yeast]", it rises because heating a gas increases in pressure, and the dough expands because of that pressure. Yes, the heat also kills the yeast, but that has nothing to do with oven spring.
(And of course, the spring only "sticks" if the dough is both elastic enough to permit that expansion -for example because it has a gluten network- and developed enough that, in that expanded state, the dough can set well enough to support its own shape, rather than deflating once we remove the heat, and the high pressure gasses cool down and contract, pull the now baked bread in on itself)