Number crunching? Beyond spreadsheets and some small custom simulation programs, I doubt anyone used the Spectrum for that. In the 80s if you wanted to do heavy number crunching you at least bought something with a floating-point unit.
Home computers were used sporadically for industrial control, usually in small or one-off designs. I know of examples where the Apple II and Commodore 64 were used for industrial control in factories; I'd be shocked if no one ever used the ZX Spectrum.
I'll embrace the unusual spirit of your question: could the ZX Spectrum run an entire space-based warship?
I think the answer is actually a qualified yes. A 3.5 MHz Z80 with 64 KB of RAM runs circles around the Apollo Guidance Computer, which was sufficient to guide a small craft to the Moon and back autonomously. It's considerably more computational power than existed in the first fly-by-wire aircraft.
Connecting the darn thing to hundreds of control systems would be an interesting electronics challenge, but doable. The software would be a spectacular project and by far the most involved aspect. Yes, it's a slow machine. But with the right software, there's no reason a Speccy couldn't juggle, for example, 100 real time tasks, each requiring an update once per second on average. That leaves ~1000 instructions per task per second, very roughly, which is enough to do several floating point calculations or dozens of high precision fixed point calculations, or test and control dozens of IO channels, in each task, every second.
This comes up sometimes with the Apollo Guidance Computer. How could such a tiny computer control a spacecraft? We tend to forget that even tiny computers are blazing-fast in human terms.