For a more fun answer than an exam, consider that the real estate on a CPU is typically dominated by two things, cache and out-of-order speculation hardware(predictors and such). Then, turning off speculative execution would be like turning off a third of your CPU. As to the actual performance impact, it'd be massive. There's a reason why no modern processor is in-order.
No modern performance-oriented processor, that is. Plenty of low-power, area-constrained embedded ones still are. The Intel Quark series of SoCs, for example. Those are basically a very fast 486, with the same 5-stage in-order pipeline. (For some amusement, get Quark datasheet and compare it with the 486 datasheet --- some of the microarchitecture diagrams are identical, and some clearly had only "Intel486" replaced roughly with "IntelQuark".)
out-of-order is just one way that a hardware vendor choose to increase performance. Mill choose an other way.
You can still have out-of-order execution without branch prediction.
That said, I'm inclined to believe you're right about a massive performance impact (for many programs at least).